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Simplifying 5x2 + -8x + -32 = 0 Reorder the terms: -32 + -8x + 5x2 = 0 Solving -32 + -8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.4 + -1.6x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + -1.6x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + -1.6x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + -1.6x + x2 = 0 + 6.4 -1.6x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 -1.6x + x2 = 6.4 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 = 6.4 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 6.4 + 0.64 Combine like terms: 6.4 + 0.64 = 7.04 0.64 + -1.6x + x2 = 7.04 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 7.04 Calculate the square root of the right side: 2.653299832 Break this problem into two subproblems by setting (x + -0.8) equal to 2.653299832 and -2.653299832.Subproblem 1
x + -0.8 = 2.653299832 Simplifying x + -0.8 = 2.653299832 Reorder the terms: -0.8 + x = 2.653299832 Solving -0.8 + x = 2.653299832 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 = 2.653299832 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 2.653299832 + 0.8 x = 2.653299832 + 0.8 Combine like terms: 2.653299832 + 0.8 = 3.453299832 x = 3.453299832 Simplifying x = 3.453299832Subproblem 2
x + -0.8 = -2.653299832 Simplifying x + -0.8 = -2.653299832 Reorder the terms: -0.8 + x = -2.653299832 Solving -0.8 + x = -2.653299832 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 = -2.653299832 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -2.653299832 + 0.8 x = -2.653299832 + 0.8 Combine like terms: -2.653299832 + 0.8 = -1.853299832 x = -1.853299832 Simplifying x = -1.853299832Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.453299832, -1.853299832}
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