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Simplifying 4x2 + 25x + -15 = 0 Reorder the terms: -15 + 25x + 4x2 = 0 Solving -15 + 25x + 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 + 6.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 6.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 6.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 6.25x + x2 = 0 + 3.75 6.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 6.25x + x2 = 3.75 The x term is 6.25x. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25x + 9.765625 + x2 = 3.75 + 9.765625 Reorder the terms: 9.765625 + 6.25x + x2 = 3.75 + 9.765625 Combine like terms: 3.75 + 9.765625 = 13.515625 9.765625 + 6.25x + x2 = 13.515625 Factor a perfect square on the left side: (x + 3.125)(x + 3.125) = 13.515625 Calculate the square root of the right side: 3.676360292 Break this problem into two subproblems by setting (x + 3.125) equal to 3.676360292 and -3.676360292.Subproblem 1
x + 3.125 = 3.676360292 Simplifying x + 3.125 = 3.676360292 Reorder the terms: 3.125 + x = 3.676360292 Solving 3.125 + x = 3.676360292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = 3.676360292 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = 3.676360292 + -3.125 x = 3.676360292 + -3.125 Combine like terms: 3.676360292 + -3.125 = 0.551360292 x = 0.551360292 Simplifying x = 0.551360292Subproblem 2
x + 3.125 = -3.676360292 Simplifying x + 3.125 = -3.676360292 Reorder the terms: 3.125 + x = -3.676360292 Solving 3.125 + x = -3.676360292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = -3.676360292 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = -3.676360292 + -3.125 x = -3.676360292 + -3.125 Combine like terms: -3.676360292 + -3.125 = -6.801360292 x = -6.801360292 Simplifying x = -6.801360292Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.551360292, -6.801360292}
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