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Solve. 10-9x^(2)+4x=-6x^(2) Choose 1 answer: (A) x=(-1+-sqrt129)/(8) (B) x=(-3+-sqrt17)/(2) (C) x=1,-(1)/(2) (D) x=(-2+-sqrt34)/(-3)

Solve.\newline10−9x2+4x=−6x210-9x^{2}+4x=-6x^{2}\newlineChoose 11 answer:\newline(A) \newlinex=−1±1298x=\frac{-1\pm\sqrt{129}}{8}\newline(B) \newlinex=−3±172x=\frac{-3\pm\sqrt{17}}{2}\newline(C) \newlinex=1,−12x=1,-\frac{1}{2}\newline(D) \newlinex=−2±34−3x=\frac{-2\pm\sqrt{34}}{-3}

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Q. Solve.\newline10−9x2+4x=−6x210-9x^{2}+4x=-6x^{2}\newlineChoose 11 answer:\newline(A) \newlinex=−1±1298x=\frac{-1\pm\sqrt{129}}{8}\newline(B) \newlinex=−3±172x=\frac{-3\pm\sqrt{17}}{2}\newline(C) \newlinex=1,−12x=1,-\frac{1}{2}\newline(D) \newlinex=−2±34−3x=\frac{-2\pm\sqrt{34}}{-3}
  1. Combine like terms: First, let's combine like terms by moving all terms to one side of the equation to set it equal to zero.\newline10−9x2+4x=−6x210 - 9x^2 + 4x = -6x^2\newlineAdd 6x26x^2 to both sides to combine the x2x^2 terms.\newline10−9x2+6x2+4x=010 - 9x^2 + 6x^2 + 4x = 0\newlineSimplify the equation.\newline10−3x2+4x=010 - 3x^2 + 4x = 0
  2. Rearrange in standard form: Now, let's rearrange the terms in standard quadratic form ax2+bx+c=0ax^2 + bx + c = 0.\newline−3x2+4x+10=0-3x^2 + 4x + 10 = 0
  3. Identify coefficients: We need to solve for x using the quadratic formula, x = \frac{{-b \pm \sqrt{{b^22 - 44ac}}}}{{22a}}. First, identify the coefficients a, b, and c.\newlinea = −3-3, b = 44, c = 1010
  4. Substitute into quadratic formula: Now, substitute the values of aa, bb, and cc into the quadratic formula.x=−(4)±(4)2−4(−3)(10)2(−3)x = \frac{{-\left(4\right) \pm \sqrt{{\left(4\right)^2 - 4\left(-3\right)\left(10\right)}}}}{{2\left(-3\right)}}
  5. Calculate discriminant: Calculate the discriminant (the part under the square root).\newlineDiscriminant = (4)2−4(−3)(10)(4)^2 - 4(-3)(10)\newlineDiscriminant = 16+12016 + 120\newlineDiscriminant = 136136
  6. Substitute discriminant into formula: Now, substitute the discriminant back into the quadratic formula. \newlinex=−4±136−6x = \frac{{-4 \pm \sqrt{{136}}}}{{-6}}
  7. Simplify square root: Simplify the square root of the discriminant. 136=4×34=2×34\sqrt{136} = \sqrt{4 \times 34} = 2 \times \sqrt{34}
  8. Substitute simplified square root: Substitute the simplified square root back into the quadratic formula. x=−4±2⋅34−6x = \frac{{-4 \pm 2 \cdot \sqrt{34}}}{{-6}}
  9. Divide all terms by −2-2: Now, simplify the equation by dividing all terms by −2-2 to make the denominator positive.\newlinex=2±343x = \frac{2 \pm \sqrt{34}}{3}
  10. Final answer: The final answer is in the form of two possible solutions for xx.x=2+343x = \frac{{2 + \sqrt{{34}}}}{3} or x=2−343x = \frac{{2 - \sqrt{{34}}}}{3}

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