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Simplifying 8x2 + -40x = 25 Reorder the terms: -40x + 8x2 = 25 Solving -40x + 8x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -40x + 8x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -40x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + -5x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -5x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -5x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -5x + x2 = 0 + 3.125 -5x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -5x + x2 = 3.125 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 3.125 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 3.125 + 6.25 Combine like terms: 3.125 + 6.25 = 9.375 6.25 + -5x + x2 = 9.375 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 9.375 Calculate the square root of the right side: 3.061862178 Break this problem into two subproblems by setting (x + -2.5) equal to 3.061862178 and -3.061862178.Subproblem 1
x + -2.5 = 3.061862178 Simplifying x + -2.5 = 3.061862178 Reorder the terms: -2.5 + x = 3.061862178 Solving -2.5 + x = 3.061862178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.061862178 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.061862178 + 2.5 x = 3.061862178 + 2.5 Combine like terms: 3.061862178 + 2.5 = 5.561862178 x = 5.561862178 Simplifying x = 5.561862178Subproblem 2
x + -2.5 = -3.061862178 Simplifying x + -2.5 = -3.061862178 Reorder the terms: -2.5 + x = -3.061862178 Solving -2.5 + x = -3.061862178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.061862178 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.061862178 + 2.5 x = -3.061862178 + 2.5 Combine like terms: -3.061862178 + 2.5 = -0.561862178 x = -0.561862178 Simplifying x = -0.561862178Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.561862178, -0.561862178}
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