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Simplifying 2x2 + 3x2 + -8x = 12 Reorder the terms: -8x + 2x2 + 3x2 = 12 Combine like terms: 2x2 + 3x2 = 5x2 -8x + 5x2 = 12 Solving -8x + 5x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -8x + 5x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -1.6x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -1.6x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -1.6x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -1.6x + x2 = 0 + 2.4 -1.6x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -1.6x + x2 = 2.4 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 = 2.4 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 2.4 + 0.64 Combine like terms: 2.4 + 0.64 = 3.04 0.64 + -1.6x + x2 = 3.04 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (x + -0.8) equal to 1.743559577 and -1.743559577.Subproblem 1
x + -0.8 = 1.743559577 Simplifying x + -0.8 = 1.743559577 Reorder the terms: -0.8 + x = 1.743559577 Solving -0.8 + x = 1.743559577 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 = 1.743559577 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.743559577 + 0.8 x = 1.743559577 + 0.8 Combine like terms: 1.743559577 + 0.8 = 2.543559577 x = 2.543559577 Simplifying x = 2.543559577Subproblem 2
x + -0.8 = -1.743559577 Simplifying x + -0.8 = -1.743559577 Reorder the terms: -0.8 + x = -1.743559577 Solving -0.8 + x = -1.743559577 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 = -1.743559577 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.743559577 + 0.8 x = -1.743559577 + 0.8 Combine like terms: -1.743559577 + 0.8 = -0.943559577 x = -0.943559577 Simplifying x = -0.943559577Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.543559577, -0.943559577}
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