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Simplifying 15x2 + -15x + -16 = 0 Reorder the terms: -16 + -15x + 15x2 = 0 Solving -16 + -15x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.066666667 + -1x + x2 = 0 Move the constant term to the right: Add '1.066666667' to each side of the equation. -1.066666667 + -1x + 1.066666667 + x2 = 0 + 1.066666667 Reorder the terms: -1.066666667 + 1.066666667 + -1x + x2 = 0 + 1.066666667 Combine like terms: -1.066666667 + 1.066666667 = 0.000000000 0.000000000 + -1x + x2 = 0 + 1.066666667 -1x + x2 = 0 + 1.066666667 Combine like terms: 0 + 1.066666667 = 1.066666667 -1x + x2 = 1.066666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.066666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.066666667 + 0.25 Combine like terms: 1.066666667 + 0.25 = 1.316666667 0.25 + -1x + x2 = 1.316666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.316666667 Calculate the square root of the right side: 1.147460965 Break this problem into two subproblems by setting (x + -0.5) equal to 1.147460965 and -1.147460965.Subproblem 1
x + -0.5 = 1.147460965 Simplifying x + -0.5 = 1.147460965 Reorder the terms: -0.5 + x = 1.147460965 Solving -0.5 + x = 1.147460965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.147460965 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.147460965 + 0.5 x = 1.147460965 + 0.5 Combine like terms: 1.147460965 + 0.5 = 1.647460965 x = 1.647460965 Simplifying x = 1.647460965Subproblem 2
x + -0.5 = -1.147460965 Simplifying x + -0.5 = -1.147460965 Reorder the terms: -0.5 + x = -1.147460965 Solving -0.5 + x = -1.147460965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.147460965 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.147460965 + 0.5 x = -1.147460965 + 0.5 Combine like terms: -1.147460965 + 0.5 = -0.647460965 x = -0.647460965 Simplifying x = -0.647460965Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.647460965, -0.647460965}
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