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Simplifying 2x(3x + -12) = (4x + 9) Reorder the terms: 2x(-12 + 3x) = (4x + 9) (-12 * 2x + 3x * 2x) = (4x + 9) (-24x + 6x2) = (4x + 9) Reorder the terms: -24x + 6x2 = (9 + 4x) Remove parenthesis around (9 + 4x) -24x + 6x2 = 9 + 4x Solving -24x + 6x2 = 9 + 4x Solving for variable 'x'. Reorder the terms: -9 + -24x + -4x + 6x2 = 9 + 4x + -9 + -4x Combine like terms: -24x + -4x = -28x -9 + -28x + 6x2 = 9 + 4x + -9 + -4x Reorder the terms: -9 + -28x + 6x2 = 9 + -9 + 4x + -4x Combine like terms: 9 + -9 = 0 -9 + -28x + 6x2 = 0 + 4x + -4x -9 + -28x + 6x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -9 + -28x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -4.666666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -4.666666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -4.666666667x + x2 = 0 + 1.5 -4.666666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -4.666666667x + x2 = 1.5 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 1.5 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 1.5 + 5.444444448 Combine like terms: 1.5 + 5.444444448 = 6.944444448 5.444444448 + -4.666666667x + x2 = 6.944444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 6.944444448 Calculate the square root of the right side: 2.635231384 Break this problem into two subproblems by setting (x + -2.333333334) equal to 2.635231384 and -2.635231384.Subproblem 1
x + -2.333333334 = 2.635231384 Simplifying x + -2.333333334 = 2.635231384 Reorder the terms: -2.333333334 + x = 2.635231384 Solving -2.333333334 + x = 2.635231384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 2.635231384 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 2.635231384 + 2.333333334 x = 2.635231384 + 2.333333334 Combine like terms: 2.635231384 + 2.333333334 = 4.968564718 x = 4.968564718 Simplifying x = 4.968564718Subproblem 2
x + -2.333333334 = -2.635231384 Simplifying x + -2.333333334 = -2.635231384 Reorder the terms: -2.333333334 + x = -2.635231384 Solving -2.333333334 + x = -2.635231384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -2.635231384 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -2.635231384 + 2.333333334 x = -2.635231384 + 2.333333334 Combine like terms: -2.635231384 + 2.333333334 = -0.30189805 x = -0.30189805 Simplifying x = -0.30189805Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.968564718, -0.30189805}
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