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Simplifying 7x(15 + -1x) = 21 (15 * 7x + -1x * 7x) = 21 (105x + -7x2) = 21 Solving 105x + -7x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 105x + -7x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 105x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-3 + 15x + -1x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-3 + 15x + -1x2)' equal to zero and attempt to solve: Simplifying -3 + 15x + -1x2 = 0 Solving -3 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -15x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -15x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -15x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -15x + x2 = 0 + -3 -15x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -15x + x2 = -3 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -3 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -3 + 56.25 Combine like terms: -3 + 56.25 = 53.25 56.25 + -15x + x2 = 53.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 53.25 Calculate the square root of the right side: 7.29725976 Break this problem into two subproblems by setting (x + -7.5) equal to 7.29725976 and -7.29725976.Subproblem 1
x + -7.5 = 7.29725976 Simplifying x + -7.5 = 7.29725976 Reorder the terms: -7.5 + x = 7.29725976 Solving -7.5 + x = 7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.29725976 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.29725976 + 7.5 x = 7.29725976 + 7.5 Combine like terms: 7.29725976 + 7.5 = 14.79725976 x = 14.79725976 Simplifying x = 14.79725976Subproblem 2
x + -7.5 = -7.29725976 Simplifying x + -7.5 = -7.29725976 Reorder the terms: -7.5 + x = -7.29725976 Solving -7.5 + x = -7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.29725976 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.29725976 + 7.5 x = -7.29725976 + 7.5 Combine like terms: -7.29725976 + 7.5 = 0.20274024 x = 0.20274024 Simplifying x = 0.20274024Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.79725976, 0.20274024}Solution
x = {14.79725976, 0.20274024}
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