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Simplifying 0 = -1.86x2 + 15x + 25 Reorder the terms: 0 = 25 + 15x + -1.86x2 Solving 0 = 25 + 15x + -1.86x2 Solving for variable 'x'. Combine like terms: 0 + -25 = -25 -25 + -15x + 1.86x2 = 25 + 15x + -1.86x2 + -25 + -15x + 1.86x2 Reorder the terms: -25 + -15x + 1.86x2 = 25 + -25 + 15x + -15x + -1.86x2 + 1.86x2 Combine like terms: 25 + -25 = 0 -25 + -15x + 1.86x2 = 0 + 15x + -15x + -1.86x2 + 1.86x2 -25 + -15x + 1.86x2 = 15x + -15x + -1.86x2 + 1.86x2 Combine like terms: 15x + -15x = 0 -25 + -15x + 1.86x2 = 0 + -1.86x2 + 1.86x2 -25 + -15x + 1.86x2 = -1.86x2 + 1.86x2 Combine like terms: -1.86x2 + 1.86x2 = 0.00 -25 + -15x + 1.86x2 = 0.00 Begin completing the square. Divide all terms by 1.86 the coefficient of the squared term: Divide each side by '1.86'. -13.44086022 + -8.064516129x + x2 = 0 Move the constant term to the right: Add '13.44086022' to each side of the equation. -13.44086022 + -8.064516129x + 13.44086022 + x2 = 0 + 13.44086022 Reorder the terms: -13.44086022 + 13.44086022 + -8.064516129x + x2 = 0 + 13.44086022 Combine like terms: -13.44086022 + 13.44086022 = 0.00000000 0.00000000 + -8.064516129x + x2 = 0 + 13.44086022 -8.064516129x + x2 = 0 + 13.44086022 Combine like terms: 0 + 13.44086022 = 13.44086022 -8.064516129x + x2 = 13.44086022 The x term is -8.064516129x. Take half its coefficient (-4.032258065). Square it (16.25910510) and add it to both sides. Add '16.25910510' to each side of the equation. -8.064516129x + 16.25910510 + x2 = 13.44086022 + 16.25910510 Reorder the terms: 16.25910510 + -8.064516129x + x2 = 13.44086022 + 16.25910510 Combine like terms: 13.44086022 + 16.25910510 = 29.69996532 16.25910510 + -8.064516129x + x2 = 29.69996532 Factor a perfect square on the left side: (x + -4.032258065)(x + -4.032258065) = 29.69996532 Calculate the square root of the right side: 5.449767456 Break this problem into two subproblems by setting (x + -4.032258065) equal to 5.449767456 and -5.449767456.Subproblem 1
x + -4.032258065 = 5.449767456 Simplifying x + -4.032258065 = 5.449767456 Reorder the terms: -4.032258065 + x = 5.449767456 Solving -4.032258065 + x = 5.449767456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + x = 5.449767456 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + x = 5.449767456 + 4.032258065 x = 5.449767456 + 4.032258065 Combine like terms: 5.449767456 + 4.032258065 = 9.482025521 x = 9.482025521 Simplifying x = 9.482025521Subproblem 2
x + -4.032258065 = -5.449767456 Simplifying x + -4.032258065 = -5.449767456 Reorder the terms: -4.032258065 + x = -5.449767456 Solving -4.032258065 + x = -5.449767456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + x = -5.449767456 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + x = -5.449767456 + 4.032258065 x = -5.449767456 + 4.032258065 Combine like terms: -5.449767456 + 4.032258065 = -1.417509391 x = -1.417509391 Simplifying x = -1.417509391Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.482025521, -1.417509391}
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