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Simplifying 0 = 15x2 + -24x + -32 Reorder the terms: 0 = -32 + -24x + 15x2 Solving 0 = -32 + -24x + 15x2 Solving for variable 'x'. Combine like terms: 0 + 32 = 32 32 + 24x + -15x2 = -32 + -24x + 15x2 + 32 + 24x + -15x2 Reorder the terms: 32 + 24x + -15x2 = -32 + 32 + -24x + 24x + 15x2 + -15x2 Combine like terms: -32 + 32 = 0 32 + 24x + -15x2 = 0 + -24x + 24x + 15x2 + -15x2 32 + 24x + -15x2 = -24x + 24x + 15x2 + -15x2 Combine like terms: -24x + 24x = 0 32 + 24x + -15x2 = 0 + 15x2 + -15x2 32 + 24x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 32 + 24x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -2.133333333 + -1.6x + x2 = 0 Move the constant term to the right: Add '2.133333333' to each side of the equation. -2.133333333 + -1.6x + 2.133333333 + x2 = 0 + 2.133333333 Reorder the terms: -2.133333333 + 2.133333333 + -1.6x + x2 = 0 + 2.133333333 Combine like terms: -2.133333333 + 2.133333333 = 0.000000000 0.000000000 + -1.6x + x2 = 0 + 2.133333333 -1.6x + x2 = 0 + 2.133333333 Combine like terms: 0 + 2.133333333 = 2.133333333 -1.6x + x2 = 2.133333333 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 2.133333333 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 2.133333333 + 0.64 Combine like terms: 2.133333333 + 0.64 = 2.773333333 0.64 + -1.6x + x2 = 2.773333333 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 2.773333333 Calculate the square root of the right side: 1.665332799 Break this problem into two subproblems by setting (x + -0.8) equal to 1.665332799 and -1.665332799.Subproblem 1
x + -0.8 = 1.665332799 Simplifying x + -0.8 = 1.665332799 Reorder the terms: -0.8 + x = 1.665332799 Solving -0.8 + x = 1.665332799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.665332799 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.665332799 + 0.8 x = 1.665332799 + 0.8 Combine like terms: 1.665332799 + 0.8 = 2.465332799 x = 2.465332799 Simplifying x = 2.465332799Subproblem 2
x + -0.8 = -1.665332799 Simplifying x + -0.8 = -1.665332799 Reorder the terms: -0.8 + x = -1.665332799 Solving -0.8 + x = -1.665332799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.665332799 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.665332799 + 0.8 x = -1.665332799 + 0.8 Combine like terms: -1.665332799 + 0.8 = -0.865332799 x = -0.865332799 Simplifying x = -0.865332799Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.465332799, -0.865332799}
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