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Simplifying 2x + -3(2x + -9) = 6(3x + -8) * 8x Reorder the terms: 2x + -3(-9 + 2x) = 6(3x + -8) * 8x 2x + (-9 * -3 + 2x * -3) = 6(3x + -8) * 8x 2x + (27 + -6x) = 6(3x + -8) * 8x Reorder the terms: 27 + 2x + -6x = 6(3x + -8) * 8x Combine like terms: 2x + -6x = -4x 27 + -4x = 6(3x + -8) * 8x Reorder the terms: 27 + -4x = 6(-8 + 3x) * 8x Reorder the terms for easier multiplication: 27 + -4x = 6 * 8x(-8 + 3x) Multiply 6 * 8 27 + -4x = 48x(-8 + 3x) 27 + -4x = (-8 * 48x + 3x * 48x) 27 + -4x = (-384x + 144x2) Solving 27 + -4x = -384x + 144x2 Solving for variable 'x'. Combine like terms: -4x + 384x = 380x 27 + 380x + -144x2 = -384x + 144x2 + 384x + -144x2 Reorder the terms: 27 + 380x + -144x2 = -384x + 384x + 144x2 + -144x2 Combine like terms: -384x + 384x = 0 27 + 380x + -144x2 = 0 + 144x2 + -144x2 27 + 380x + -144x2 = 144x2 + -144x2 Combine like terms: 144x2 + -144x2 = 0 27 + 380x + -144x2 = 0 Begin completing the square. Divide all terms by -144 the coefficient of the squared term: Divide each side by '-144'. -0.1875 + -2.638888889x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -2.638888889x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -2.638888889x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -2.638888889x + x2 = 0 + 0.1875 -2.638888889x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -2.638888889x + x2 = 0.1875 The x term is -2.638888889x. Take half its coefficient (-1.319444445). Square it (1.740933643) and add it to both sides. Add '1.740933643' to each side of the equation. -2.638888889x + 1.740933643 + x2 = 0.1875 + 1.740933643 Reorder the terms: 1.740933643 + -2.638888889x + x2 = 0.1875 + 1.740933643 Combine like terms: 0.1875 + 1.740933643 = 1.928433643 1.740933643 + -2.638888889x + x2 = 1.928433643 Factor a perfect square on the left side: (x + -1.319444445)(x + -1.319444445) = 1.928433643 Calculate the square root of the right side: 1.38868054 Break this problem into two subproblems by setting (x + -1.319444445) equal to 1.38868054 and -1.38868054.Subproblem 1
x + -1.319444445 = 1.38868054 Simplifying x + -1.319444445 = 1.38868054 Reorder the terms: -1.319444445 + x = 1.38868054 Solving -1.319444445 + x = 1.38868054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.319444445' to each side of the equation. -1.319444445 + 1.319444445 + x = 1.38868054 + 1.319444445 Combine like terms: -1.319444445 + 1.319444445 = 0.000000000 0.000000000 + x = 1.38868054 + 1.319444445 x = 1.38868054 + 1.319444445 Combine like terms: 1.38868054 + 1.319444445 = 2.708124985 x = 2.708124985 Simplifying x = 2.708124985Subproblem 2
x + -1.319444445 = -1.38868054 Simplifying x + -1.319444445 = -1.38868054 Reorder the terms: -1.319444445 + x = -1.38868054 Solving -1.319444445 + x = -1.38868054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.319444445' to each side of the equation. -1.319444445 + 1.319444445 + x = -1.38868054 + 1.319444445 Combine like terms: -1.319444445 + 1.319444445 = 0.000000000 0.000000000 + x = -1.38868054 + 1.319444445 x = -1.38868054 + 1.319444445 Combine like terms: -1.38868054 + 1.319444445 = -0.069236095 x = -0.069236095 Simplifying x = -0.069236095Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.708124985, -0.069236095}
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