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Simplifying 3(x + -4) + -4x = 4(x + -3) * 5x Reorder the terms: 3(-4 + x) + -4x = 4(x + -3) * 5x (-4 * 3 + x * 3) + -4x = 4(x + -3) * 5x (-12 + 3x) + -4x = 4(x + -3) * 5x Combine like terms: 3x + -4x = -1x -12 + -1x = 4(x + -3) * 5x Reorder the terms: -12 + -1x = 4(-3 + x) * 5x Reorder the terms for easier multiplication: -12 + -1x = 4 * 5x(-3 + x) Multiply 4 * 5 -12 + -1x = 20x(-3 + x) -12 + -1x = (-3 * 20x + x * 20x) -12 + -1x = (-60x + 20x2) Solving -12 + -1x = -60x + 20x2 Solving for variable 'x'. Combine like terms: -1x + 60x = 59x -12 + 59x + -20x2 = -60x + 20x2 + 60x + -20x2 Reorder the terms: -12 + 59x + -20x2 = -60x + 60x + 20x2 + -20x2 Combine like terms: -60x + 60x = 0 -12 + 59x + -20x2 = 0 + 20x2 + -20x2 -12 + 59x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -12 + 59x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. 0.6 + -2.95x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -2.95x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -2.95x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -2.95x + x2 = 0 + -0.6 -2.95x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -2.95x + x2 = -0.6 The x term is -2.95x. Take half its coefficient (-1.475). Square it (2.175625) and add it to both sides. Add '2.175625' to each side of the equation. -2.95x + 2.175625 + x2 = -0.6 + 2.175625 Reorder the terms: 2.175625 + -2.95x + x2 = -0.6 + 2.175625 Combine like terms: -0.6 + 2.175625 = 1.575625 2.175625 + -2.95x + x2 = 1.575625 Factor a perfect square on the left side: (x + -1.475)(x + -1.475) = 1.575625 Calculate the square root of the right side: 1.255239021 Break this problem into two subproblems by setting (x + -1.475) equal to 1.255239021 and -1.255239021.Subproblem 1
x + -1.475 = 1.255239021 Simplifying x + -1.475 = 1.255239021 Reorder the terms: -1.475 + x = 1.255239021 Solving -1.475 + x = 1.255239021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.475' to each side of the equation. -1.475 + 1.475 + x = 1.255239021 + 1.475 Combine like terms: -1.475 + 1.475 = 0.000 0.000 + x = 1.255239021 + 1.475 x = 1.255239021 + 1.475 Combine like terms: 1.255239021 + 1.475 = 2.730239021 x = 2.730239021 Simplifying x = 2.730239021Subproblem 2
x + -1.475 = -1.255239021 Simplifying x + -1.475 = -1.255239021 Reorder the terms: -1.475 + x = -1.255239021 Solving -1.475 + x = -1.255239021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.475' to each side of the equation. -1.475 + 1.475 + x = -1.255239021 + 1.475 Combine like terms: -1.475 + 1.475 = 0.000 0.000 + x = -1.255239021 + 1.475 x = -1.255239021 + 1.475 Combine like terms: -1.255239021 + 1.475 = 0.219760979 x = 0.219760979 Simplifying x = 0.219760979Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.730239021, 0.219760979}
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