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Simplifying 2x(3x + -5) = 9x + 15 Reorder the terms: 2x(-5 + 3x) = 9x + 15 (-5 * 2x + 3x * 2x) = 9x + 15 (-10x + 6x2) = 9x + 15 Reorder the terms: -10x + 6x2 = 15 + 9x Solving -10x + 6x2 = 15 + 9x Solving for variable 'x'. Reorder the terms: -15 + -10x + -9x + 6x2 = 15 + 9x + -15 + -9x Combine like terms: -10x + -9x = -19x -15 + -19x + 6x2 = 15 + 9x + -15 + -9x Reorder the terms: -15 + -19x + 6x2 = 15 + -15 + 9x + -9x Combine like terms: 15 + -15 = 0 -15 + -19x + 6x2 = 0 + 9x + -9x -15 + -19x + 6x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -15 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.166666667x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.166666667x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.166666667x + x2 = 0 + 2.5 -3.166666667x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.166666667x + x2 = 2.5 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = 2.5 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 2.5 + 2.506944447 Combine like terms: 2.5 + 2.506944447 = 5.006944447 2.506944447 + -3.166666667x + x2 = 5.006944447 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 5.006944447 Calculate the square root of the right side: 2.237620264 Break this problem into two subproblems by setting (x + -1.583333334) equal to 2.237620264 and -2.237620264.Subproblem 1
x + -1.583333334 = 2.237620264 Simplifying x + -1.583333334 = 2.237620264 Reorder the terms: -1.583333334 + x = 2.237620264 Solving -1.583333334 + x = 2.237620264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 2.237620264 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 2.237620264 + 1.583333334 x = 2.237620264 + 1.583333334 Combine like terms: 2.237620264 + 1.583333334 = 3.820953598 x = 3.820953598 Simplifying x = 3.820953598Subproblem 2
x + -1.583333334 = -2.237620264 Simplifying x + -1.583333334 = -2.237620264 Reorder the terms: -1.583333334 + x = -2.237620264 Solving -1.583333334 + x = -2.237620264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -2.237620264 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -2.237620264 + 1.583333334 x = -2.237620264 + 1.583333334 Combine like terms: -2.237620264 + 1.583333334 = -0.65428693 x = -0.65428693 Simplifying x = -0.65428693Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.820953598, -0.65428693}
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