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Simplifying 8x + -7 = 5x(x + -2) Reorder the terms: -7 + 8x = 5x(x + -2) Reorder the terms: -7 + 8x = 5x(-2 + x) -7 + 8x = (-2 * 5x + x * 5x) -7 + 8x = (-10x + 5x2) Solving -7 + 8x = -10x + 5x2 Solving for variable 'x'. Combine like terms: 8x + 10x = 18x -7 + 18x + -5x2 = -10x + 5x2 + 10x + -5x2 Reorder the terms: -7 + 18x + -5x2 = -10x + 10x + 5x2 + -5x2 Combine like terms: -10x + 10x = 0 -7 + 18x + -5x2 = 0 + 5x2 + -5x2 -7 + 18x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -7 + 18x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.4 + -3.6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -3.6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -3.6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -3.6x + x2 = 0 + -1.4 -3.6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -3.6x + x2 = -1.4 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -1.4 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -1.4 + 3.24 Combine like terms: -1.4 + 3.24 = 1.84 3.24 + -3.6x + x2 = 1.84 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + -1.8) equal to 1.356465997 and -1.356465997.Subproblem 1
x + -1.8 = 1.356465997 Simplifying x + -1.8 = 1.356465997 Reorder the terms: -1.8 + x = 1.356465997 Solving -1.8 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 1.356465997 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 1.356465997 + 1.8 x = 1.356465997 + 1.8 Combine like terms: 1.356465997 + 1.8 = 3.156465997 x = 3.156465997 Simplifying x = 3.156465997Subproblem 2
x + -1.8 = -1.356465997 Simplifying x + -1.8 = -1.356465997 Reorder the terms: -1.8 + x = -1.356465997 Solving -1.8 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -1.356465997 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -1.356465997 + 1.8 x = -1.356465997 + 1.8 Combine like terms: -1.356465997 + 1.8 = 0.443534003 x = 0.443534003 Simplifying x = 0.443534003Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.156465997, 0.443534003}
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