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Simplifying 1515 = x(10x + -13) Reorder the terms: 1515 = x(-13 + 10x) 1515 = (-13 * x + 10x * x) 1515 = (-13x + 10x2) Solving 1515 = -13x + 10x2 Solving for variable 'x'. Reorder the terms: 1515 + 13x + -10x2 = -13x + 13x + 10x2 + -10x2 Combine like terms: -13x + 13x = 0 1515 + 13x + -10x2 = 0 + 10x2 + -10x2 1515 + 13x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 1515 + 13x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -151.5 + -1.3x + x2 = 0 Move the constant term to the right: Add '151.5' to each side of the equation. -151.5 + -1.3x + 151.5 + x2 = 0 + 151.5 Reorder the terms: -151.5 + 151.5 + -1.3x + x2 = 0 + 151.5 Combine like terms: -151.5 + 151.5 = 0.0 0.0 + -1.3x + x2 = 0 + 151.5 -1.3x + x2 = 0 + 151.5 Combine like terms: 0 + 151.5 = 151.5 -1.3x + x2 = 151.5 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = 151.5 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = 151.5 + 0.4225 Combine like terms: 151.5 + 0.4225 = 151.9225 0.4225 + -1.3x + x2 = 151.9225 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = 151.9225 Calculate the square root of the right side: 12.325684565 Break this problem into two subproblems by setting (x + -0.65) equal to 12.325684565 and -12.325684565.Subproblem 1
x + -0.65 = 12.325684565 Simplifying x + -0.65 = 12.325684565 Reorder the terms: -0.65 + x = 12.325684565 Solving -0.65 + x = 12.325684565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = 12.325684565 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 12.325684565 + 0.65 x = 12.325684565 + 0.65 Combine like terms: 12.325684565 + 0.65 = 12.975684565 x = 12.975684565 Simplifying x = 12.975684565Subproblem 2
x + -0.65 = -12.325684565 Simplifying x + -0.65 = -12.325684565 Reorder the terms: -0.65 + x = -12.325684565 Solving -0.65 + x = -12.325684565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = -12.325684565 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -12.325684565 + 0.65 x = -12.325684565 + 0.65 Combine like terms: -12.325684565 + 0.65 = -11.675684565 x = -11.675684565 Simplifying x = -11.675684565Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.975684565, -11.675684565}
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