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Simplifying 5x2 + -8x = 10 Reorder the terms: -8x + 5x2 = 10 Solving -8x + 5x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -8x + 5x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -1.6x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.6x + x2 = 0 + 2 -1.6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.6x + x2 = 2 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 2 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 2 + 0.64 Combine like terms: 2 + 0.64 = 2.64 0.64 + -1.6x + x2 = 2.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (x + -0.8) equal to 1.624807681 and -1.624807681.Subproblem 1
x + -0.8 = 1.624807681 Simplifying x + -0.8 = 1.624807681 Reorder the terms: -0.8 + x = 1.624807681 Solving -0.8 + x = 1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.624807681 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.624807681 + 0.8 x = 1.624807681 + 0.8 Combine like terms: 1.624807681 + 0.8 = 2.424807681 x = 2.424807681 Simplifying x = 2.424807681Subproblem 2
x + -0.8 = -1.624807681 Simplifying x + -0.8 = -1.624807681 Reorder the terms: -0.8 + x = -1.624807681 Solving -0.8 + x = -1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.624807681 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.624807681 + 0.8 x = -1.624807681 + 0.8 Combine like terms: -1.624807681 + 0.8 = -0.824807681 x = -0.824807681 Simplifying x = -0.824807681Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.424807681, -0.824807681}
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