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Simplifying -3(-1x + 7) * 5x = -21 Reorder the terms: -3(7 + -1x) * 5x = -21 Reorder the terms for easier multiplication: -3 * 5x(7 + -1x) = -21 Multiply -3 * 5 -15x(7 + -1x) = -21 (7 * -15x + -1x * -15x) = -21 (-105x + 15x2) = -21 Solving -105x + 15x2 = -21 Solving for variable 'x'. Reorder the terms: 21 + -105x + 15x2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + -105x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(7 + -35x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -35x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + -35x + 5x2 = 0 Solving 7 + -35x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -7x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -7x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -7x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -7x + x2 = 0 + -1.4 -7x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -7x + x2 = -1.4 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -1.4 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1.4 + 12.25 Combine like terms: -1.4 + 12.25 = 10.85 12.25 + -7x + x2 = 10.85 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 10.85 Calculate the square root of the right side: 3.293933818 Break this problem into two subproblems by setting (x + -3.5) equal to 3.293933818 and -3.293933818.Subproblem 1
x + -3.5 = 3.293933818 Simplifying x + -3.5 = 3.293933818 Reorder the terms: -3.5 + x = 3.293933818 Solving -3.5 + x = 3.293933818 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.293933818 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.293933818 + 3.5 x = 3.293933818 + 3.5 Combine like terms: 3.293933818 + 3.5 = 6.793933818 x = 6.793933818 Simplifying x = 6.793933818Subproblem 2
x + -3.5 = -3.293933818 Simplifying x + -3.5 = -3.293933818 Reorder the terms: -3.5 + x = -3.293933818 Solving -3.5 + x = -3.293933818 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.293933818 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.293933818 + 3.5 x = -3.293933818 + 3.5 Combine like terms: -3.293933818 + 3.5 = 0.206066182 x = 0.206066182 Simplifying x = 0.206066182Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.793933818, 0.206066182}Solution
x = {6.793933818, 0.206066182}
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