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Simplifying x(2x + -5) = 130 Reorder the terms: x(-5 + 2x) = 130 (-5 * x + 2x * x) = 130 (-5x + 2x2) = 130 Solving -5x + 2x2 = 130 Solving for variable 'x'. Reorder the terms: -130 + -5x + 2x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -65 + -2.5x + x2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + -2.5x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + -2.5x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -2.5x + x2 = 0 + 65 -2.5x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 -2.5x + x2 = 65 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 65 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 65 + 1.5625 Combine like terms: 65 + 1.5625 = 66.5625 1.5625 + -2.5x + x2 = 66.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 66.5625 Calculate the square root of the right side: 8.158584436 Break this problem into two subproblems by setting (x + -1.25) equal to 8.158584436 and -8.158584436.Subproblem 1
x + -1.25 = 8.158584436 Simplifying x + -1.25 = 8.158584436 Reorder the terms: -1.25 + x = 8.158584436 Solving -1.25 + x = 8.158584436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 8.158584436 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 8.158584436 + 1.25 x = 8.158584436 + 1.25 Combine like terms: 8.158584436 + 1.25 = 9.408584436 x = 9.408584436 Simplifying x = 9.408584436Subproblem 2
x + -1.25 = -8.158584436 Simplifying x + -1.25 = -8.158584436 Reorder the terms: -1.25 + x = -8.158584436 Solving -1.25 + x = -8.158584436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -8.158584436 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -8.158584436 + 1.25 x = -8.158584436 + 1.25 Combine like terms: -8.158584436 + 1.25 = -6.908584436 x = -6.908584436 Simplifying x = -6.908584436Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.408584436, -6.908584436}
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