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Simplifying 3x(x + -5) * 3 = -30 Reorder the terms: 3x(-5 + x) * 3 = -30 Reorder the terms for easier multiplication: 3 * 3x(-5 + x) = -30 Multiply 3 * 3 9x(-5 + x) = -30 (-5 * 9x + x * 9x) = -30 (-45x + 9x2) = -30 Solving -45x + 9x2 = -30 Solving for variable 'x'. Reorder the terms: 30 + -45x + 9x2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + -45x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -15x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -15x + 3x2)' equal to zero and attempt to solve: Simplifying 10 + -15x + 3x2 = 0 Solving 10 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + -5x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -5x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -5x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + -3.333333333 -5x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -5x + x2 = -3.333333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -3.333333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -3.333333333 + 6.25 Combine like terms: -3.333333333 + 6.25 = 2.916666667 6.25 + -5x + x2 = 2.916666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2.916666667 Calculate the square root of the right side: 1.707825128 Break this problem into two subproblems by setting (x + -2.5) equal to 1.707825128 and -1.707825128.Subproblem 1
x + -2.5 = 1.707825128 Simplifying x + -2.5 = 1.707825128 Reorder the terms: -2.5 + x = 1.707825128 Solving -2.5 + x = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.707825128 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.707825128 + 2.5 x = 1.707825128 + 2.5 Combine like terms: 1.707825128 + 2.5 = 4.207825128 x = 4.207825128 Simplifying x = 4.207825128Subproblem 2
x + -2.5 = -1.707825128 Simplifying x + -2.5 = -1.707825128 Reorder the terms: -2.5 + x = -1.707825128 Solving -2.5 + x = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.707825128 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.707825128 + 2.5 x = -1.707825128 + 2.5 Combine like terms: -1.707825128 + 2.5 = 0.792174872 x = 0.792174872 Simplifying x = 0.792174872Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.207825128, 0.792174872}Solution
x = {4.207825128, 0.792174872}
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