Set Equations Equal: First, we need to set the two equations equal to each other because we are looking for the value of x where y is the same for both equations. Given equations: y = 4x^2 - 4x + 6 y = 6x^2 - x + 1 Setting them equal to each other: 4x^2 - 4x + 6 = 6x^2 - x + 1Rearrange and Subtract: Next, we need to rearrange the equation to bring all terms to one side and set it equal to zero. We do this by subtracting the left side from the right side. Subtracting the left side from the right side: 0 = 6x^2 - x + 1 - (4x^2 - 4x + 6)Simplify Equation: Now, we simplify the equation by combining like terms. Simplifying: 0 = 6x^2 - x + 1 - 4x^2 + 4x - 6 0 = 2x^2 + 3x - 5

Grade 8

Write an equation word problem

Full solution

y=4 x^{2}-4 x+6

Set Equations Equal: First, we need to set the two equations equal to each other because we are looking for the value of $x$ where $y$ is the same for both equations. $\newline$ Given equations: $\newline$ $y = 4x^2 - 4x + 6$ $\newline$ $y = 6x^2 - x + 1$ $\newline$ Setting them equal to each other: $\newline$ $4x^2 - 4x + 6 = 6x^2 - x + 1$
Rearrange and Subtract: Next, we need to rearrange the equation to bring all terms to one side and set it equal to zero. We do this by subtracting the left side from the right side. $\newline$ Subtracting the left side from the right side: $\newline$ $0 = 6x^2 - x + 1 - (4x^2 - 4x + 6)$
Simplify Equation: Now, we simplify the equation by combining like terms. $\newline$ Simplifying: $\newline$ $0 = 6x^2 - x + 1 - 4x^2 + 4x - 6$ $\newline$ $0 = 2x^2 + 3x - 5$