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Simplifying -1x + -1x(x + -21) = 5x + 7 Reorder the terms: -1x + -1x(-21 + x) = 5x + 7 -1x + (-21 * -1x + x * -1x) = 5x + 7 -1x + (21x + -1x2) = 5x + 7 Combine like terms: -1x + 21x = 20x 20x + -1x2 = 5x + 7 Reorder the terms: 20x + -1x2 = 7 + 5x Solving 20x + -1x2 = 7 + 5x Solving for variable 'x'. Reorder the terms: -7 + 20x + -5x + -1x2 = 7 + 5x + -7 + -5x Combine like terms: 20x + -5x = 15x -7 + 15x + -1x2 = 7 + 5x + -7 + -5x Reorder the terms: -7 + 15x + -1x2 = 7 + -7 + 5x + -5x Combine like terms: 7 + -7 = 0 -7 + 15x + -1x2 = 0 + 5x + -5x -7 + 15x + -1x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -7 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -15x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -15x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -15x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -15x + x2 = 0 + -7 -15x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -15x + x2 = -7 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 = -7 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -7 + 56.25 Combine like terms: -7 + 56.25 = 49.25 56.25 + -15x + x2 = 49.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + -7.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + -7.5 = 7.017834424 Simplifying x + -7.5 = 7.017834424 Reorder the terms: -7.5 + x = 7.017834424 Solving -7.5 + x = 7.017834424 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 = 7.017834424 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.017834424 + 7.5 x = 7.017834424 + 7.5 Combine like terms: 7.017834424 + 7.5 = 14.517834424 x = 14.517834424 Simplifying x = 14.517834424Subproblem 2
x + -7.5 = -7.017834424 Simplifying x + -7.5 = -7.017834424 Reorder the terms: -7.5 + x = -7.017834424 Solving -7.5 + x = -7.017834424 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 = -7.017834424 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.017834424 + 7.5 x = -7.017834424 + 7.5 Combine like terms: -7.017834424 + 7.5 = 0.482165576 x = 0.482165576 Simplifying x = 0.482165576Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.517834424, 0.482165576}
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