Solve the equation 2x^(2)+15 x+35=x^(2) to the nearest tenth. Answer: x=

Move Terms, Set Equal: First, we need to move all terms to one side of the equation to set it equal to zero. We will subtract x^2 from both sides of the equation. 2x^2 + 15x + 35 - x^2 = x^2 - x^2 This simplifies to: x^2 + 15x + 35 = 0Factor Quadratic Equation: Next, we need to factor the quadratic equation if possible. We look for two numbers that multiply to 35 and add up to 15. The numbers 5 and 7 fit this requirement. (x + 5)(x + 7) = 0Apply Zero Product Property: Now, we apply the zero product property which states that if a product of two factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero: x + 5 = 0 or x + 7 = 0Solve for x: We solve each equation for x: For x + 5 = 0, we subtract 5 from both sides: x = -5 For x + 7 = 0, we subtract 7 from both sides: x = -7 These are the two solutions to the equation.

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Q. Solve the equation

2 x^{2}+15 x+35=x^{2}

to the nearest tenth.

\newline

Answer:

x=

Move Terms, Set Equal: First, we need to move all terms to one side of the equation to set it equal to zero. We will subtract $x^2$ from both sides of the equation. $\newline$ $2x^2 + 15x + 35 - x^2 = x^2 - x^2$ $\newline$ This simplifies to: $\newline$ $x^2 + 15x + 35 = 0$
Factor Quadratic Equation: Next, we need to factor the quadratic equation if possible. We look for two numbers that multiply to $35$ and add up to $15$ . The numbers $5$ and $7$ fit this requirement. $\newline$ $(x + 5)(x + 7) = 0$
Apply Zero Product Property: Now, we apply the zero product property which states that if a product of two factors is zero, then at least one of the factors must be zero. $\newline$ So, we set each factor equal to zero: $\newline$ $x + 5 = 0$ or $x + 7 = 0$
Solve for x: We solve each equation for x: $\newline$ For $x + 5 = 0$ , we subtract $5$ from both sides: $\newline$ $x = -5$ $\newline$ For $x + 7 = 0$ , we subtract $7$ from both sides: $\newline$ $x = -7$ $\newline$ These are the two solutions to the equation.