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Simplifying (-3)(7 + -6x) = 9x(3x + -7) (7 * -3 + -6x * -3) = 9x(3x + -7) (-21 + 18x) = 9x(3x + -7) Reorder the terms: -21 + 18x = 9x(-7 + 3x) -21 + 18x = (-7 * 9x + 3x * 9x) -21 + 18x = (-63x + 27x2) Solving -21 + 18x = -63x + 27x2 Solving for variable 'x'. Combine like terms: 18x + 63x = 81x -21 + 81x + -27x2 = -63x + 27x2 + 63x + -27x2 Reorder the terms: -21 + 81x + -27x2 = -63x + 63x + 27x2 + -27x2 Combine like terms: -63x + 63x = 0 -21 + 81x + -27x2 = 0 + 27x2 + -27x2 -21 + 81x + -27x2 = 27x2 + -27x2 Combine like terms: 27x2 + -27x2 = 0 -21 + 81x + -27x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 27x + -9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 27x + -9x2)' equal to zero and attempt to solve: Simplifying -7 + 27x + -9x2 = 0 Solving -7 + 27x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.7777777778 + -3x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -3x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -3x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + -0.7777777778 -3x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -3x + x2 = -0.7777777778 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.7777777778 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.7777777778 + 2.25 Combine like terms: -0.7777777778 + 2.25 = 1.4722222222 2.25 + -3x + x2 = 1.4722222222 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.4722222222 Calculate the square root of the right side: 1.213351648 Break this problem into two subproblems by setting (x + -1.5) equal to 1.213351648 and -1.213351648.Subproblem 1
x + -1.5 = 1.213351648 Simplifying x + -1.5 = 1.213351648 Reorder the terms: -1.5 + x = 1.213351648 Solving -1.5 + x = 1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.213351648 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.213351648 + 1.5 x = 1.213351648 + 1.5 Combine like terms: 1.213351648 + 1.5 = 2.713351648 x = 2.713351648 Simplifying x = 2.713351648Subproblem 2
x + -1.5 = -1.213351648 Simplifying x + -1.5 = -1.213351648 Reorder the terms: -1.5 + x = -1.213351648 Solving -1.5 + x = -1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.213351648 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.213351648 + 1.5 x = -1.213351648 + 1.5 Combine like terms: -1.213351648 + 1.5 = 0.286648352 x = 0.286648352 Simplifying x = 0.286648352Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.713351648, 0.286648352}Solution
x = {2.713351648, 0.286648352}
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