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Simplifying 15x2 + -25x + -12 = 0 Reorder the terms: -12 + -25x + 15x2 = 0 Solving -12 + -25x + 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'. -0.8 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.666666667x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.666666667x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.666666667x + x2 = 0 + 0.8 -1.666666667x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.666666667x + x2 = 0.8 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 0.8 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 0.8 + 0.6944444447 Combine like terms: 0.8 + 0.6944444447 = 1.4944444447 0.6944444447 + -1.666666667x + x2 = 1.4944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 1.4944444447 Calculate the square root of the right side: 1.222474721 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.222474721 and -1.222474721.Subproblem 1
x + -0.8333333335 = 1.222474721 Simplifying x + -0.8333333335 = 1.222474721 Reorder the terms: -0.8333333335 + x = 1.222474721 Solving -0.8333333335 + x = 1.222474721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.222474721 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.222474721 + 0.8333333335 x = 1.222474721 + 0.8333333335 Combine like terms: 1.222474721 + 0.8333333335 = 2.0558080545 x = 2.0558080545 Simplifying x = 2.0558080545Subproblem 2
x + -0.8333333335 = -1.222474721 Simplifying x + -0.8333333335 = -1.222474721 Reorder the terms: -0.8333333335 + x = -1.222474721 Solving -0.8333333335 + x = -1.222474721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.222474721 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.222474721 + 0.8333333335 x = -1.222474721 + 0.8333333335 Combine like terms: -1.222474721 + 0.8333333335 = -0.3891413875 x = -0.3891413875 Simplifying x = -0.3891413875Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0558080545, -0.3891413875}
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