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Simplifying 15x2 + -16x + -9 = 0 Reorder the terms: -9 + -16x + 15x2 = 0 Solving -9 + -16x + 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'. -0.6 + -1.066666667x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.066666667x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.066666667x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.066666667x + x2 = 0 + 0.6 -1.066666667x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.066666667x + x2 = 0.6 The x term is -1.066666667x. Take half its coefficient (-0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. -1.066666667x + 0.2844444446 + x2 = 0.6 + 0.2844444446 Reorder the terms: 0.2844444446 + -1.066666667x + x2 = 0.6 + 0.2844444446 Combine like terms: 0.6 + 0.2844444446 = 0.8844444446 0.2844444446 + -1.066666667x + x2 = 0.8844444446 Factor a perfect square on the left side: (x + -0.5333333335)(x + -0.5333333335) = 0.8844444446 Calculate the square root of the right side: 0.940449065 Break this problem into two subproblems by setting (x + -0.5333333335) equal to 0.940449065 and -0.940449065.Subproblem 1
x + -0.5333333335 = 0.940449065 Simplifying x + -0.5333333335 = 0.940449065 Reorder the terms: -0.5333333335 + x = 0.940449065 Solving -0.5333333335 + x = 0.940449065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + x = 0.940449065 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + x = 0.940449065 + 0.5333333335 x = 0.940449065 + 0.5333333335 Combine like terms: 0.940449065 + 0.5333333335 = 1.4737823985 x = 1.4737823985 Simplifying x = 1.4737823985Subproblem 2
x + -0.5333333335 = -0.940449065 Simplifying x + -0.5333333335 = -0.940449065 Reorder the terms: -0.5333333335 + x = -0.940449065 Solving -0.5333333335 + x = -0.940449065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + x = -0.940449065 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + x = -0.940449065 + 0.5333333335 x = -0.940449065 + 0.5333333335 Combine like terms: -0.940449065 + 0.5333333335 = -0.4071157315 x = -0.4071157315 Simplifying x = -0.4071157315Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4737823985, -0.4071157315}
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