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Simplifying 1.7x2 = 15x + 15 Reorder the terms: 1.7x2 = 15 + 15x Solving 1.7x2 = 15 + 15x Solving for variable 'x'. Reorder the terms: -15 + -15x + 1.7x2 = 15 + 15x + -15 + -15x Reorder the terms: -15 + -15x + 1.7x2 = 15 + -15 + 15x + -15x Combine like terms: 15 + -15 = 0 -15 + -15x + 1.7x2 = 0 + 15x + -15x -15 + -15x + 1.7x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -15 + -15x + 1.7x2 = 0 Begin completing the square. Divide all terms by 1.7 the coefficient of the squared term: Divide each side by '1.7'. -8.823529412 + -8.823529412x + x2 = 0 Move the constant term to the right: Add '8.823529412' to each side of the equation. -8.823529412 + -8.823529412x + 8.823529412 + x2 = 0 + 8.823529412 Reorder the terms: -8.823529412 + 8.823529412 + -8.823529412x + x2 = 0 + 8.823529412 Combine like terms: -8.823529412 + 8.823529412 = 0.000000000 0.000000000 + -8.823529412x + x2 = 0 + 8.823529412 -8.823529412x + x2 = 0 + 8.823529412 Combine like terms: 0 + 8.823529412 = 8.823529412 -8.823529412x + x2 = 8.823529412 The x term is -8.823529412x. Take half its coefficient (-4.411764706). Square it (19.46366782) and add it to both sides. Add '19.46366782' to each side of the equation. -8.823529412x + 19.46366782 + x2 = 8.823529412 + 19.46366782 Reorder the terms: 19.46366782 + -8.823529412x + x2 = 8.823529412 + 19.46366782 Combine like terms: 8.823529412 + 19.46366782 = 28.287197232 19.46366782 + -8.823529412x + x2 = 28.287197232 Factor a perfect square on the left side: (x + -4.411764706)(x + -4.411764706) = 28.287197232 Calculate the square root of the right side: 5.318570976 Break this problem into two subproblems by setting (x + -4.411764706) equal to 5.318570976 and -5.318570976.Subproblem 1
x + -4.411764706 = 5.318570976 Simplifying x + -4.411764706 = 5.318570976 Reorder the terms: -4.411764706 + x = 5.318570976 Solving -4.411764706 + x = 5.318570976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.411764706' to each side of the equation. -4.411764706 + 4.411764706 + x = 5.318570976 + 4.411764706 Combine like terms: -4.411764706 + 4.411764706 = 0.000000000 0.000000000 + x = 5.318570976 + 4.411764706 x = 5.318570976 + 4.411764706 Combine like terms: 5.318570976 + 4.411764706 = 9.730335682 x = 9.730335682 Simplifying x = 9.730335682Subproblem 2
x + -4.411764706 = -5.318570976 Simplifying x + -4.411764706 = -5.318570976 Reorder the terms: -4.411764706 + x = -5.318570976 Solving -4.411764706 + x = -5.318570976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.411764706' to each side of the equation. -4.411764706 + 4.411764706 + x = -5.318570976 + 4.411764706 Combine like terms: -4.411764706 + 4.411764706 = 0.000000000 0.000000000 + x = -5.318570976 + 4.411764706 x = -5.318570976 + 4.411764706 Combine like terms: -5.318570976 + 4.411764706 = -0.90680627 x = -0.90680627 Simplifying x = -0.90680627Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.730335682, -0.90680627}
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