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Simplifying -4x2 + 10x + 15 = 0 Reorder the terms: 15 + 10x + -4x2 = 0 Solving 15 + 10x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.75 + -2.5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -2.5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -2.5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -2.5x + x2 = 0 + 3.75 -2.5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -2.5x + x2 = 3.75 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 = 3.75 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 3.75 + 1.5625 Combine like terms: 3.75 + 1.5625 = 5.3125 1.5625 + -2.5x + x2 = 5.3125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (x + -1.25) equal to 2.304886114 and -2.304886114.Subproblem 1
x + -1.25 = 2.304886114 Simplifying x + -1.25 = 2.304886114 Reorder the terms: -1.25 + x = 2.304886114 Solving -1.25 + x = 2.304886114 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 = 2.304886114 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.304886114 + 1.25 x = 2.304886114 + 1.25 Combine like terms: 2.304886114 + 1.25 = 3.554886114 x = 3.554886114 Simplifying x = 3.554886114Subproblem 2
x + -1.25 = -2.304886114 Simplifying x + -1.25 = -2.304886114 Reorder the terms: -1.25 + x = -2.304886114 Solving -1.25 + x = -2.304886114 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 = -2.304886114 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.304886114 + 1.25 x = -2.304886114 + 1.25 Combine like terms: -2.304886114 + 1.25 = -1.054886114 x = -1.054886114 Simplifying x = -1.054886114Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.554886114, -1.054886114}
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