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Simplifying 9x + 1 = 3x2 + -15 + -1x2 + -2x + -3x + -6 Reorder the terms: 1 + 9x = 3x2 + -15 + -1x2 + -2x + -3x + -6 Reorder the terms: 1 + 9x = -15 + -6 + -2x + -3x + 3x2 + -1x2 Combine like terms: -15 + -6 = -21 1 + 9x = -21 + -2x + -3x + 3x2 + -1x2 Combine like terms: -2x + -3x = -5x 1 + 9x = -21 + -5x + 3x2 + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 1 + 9x = -21 + -5x + 2x2 Solving 1 + 9x = -21 + -5x + 2x2 Solving for variable 'x'. Reorder the terms: 1 + 21 + 9x + 5x + -2x2 = -21 + -5x + 2x2 + 21 + 5x + -2x2 Combine like terms: 1 + 21 = 22 22 + 9x + 5x + -2x2 = -21 + -5x + 2x2 + 21 + 5x + -2x2 Combine like terms: 9x + 5x = 14x 22 + 14x + -2x2 = -21 + -5x + 2x2 + 21 + 5x + -2x2 Reorder the terms: 22 + 14x + -2x2 = -21 + 21 + -5x + 5x + 2x2 + -2x2 Combine like terms: -21 + 21 = 0 22 + 14x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2 22 + 14x + -2x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 22 + 14x + -2x2 = 0 + 2x2 + -2x2 22 + 14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 22 + 14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying 11 + 7x + -1x2 = 0 Solving 11 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -7x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -7x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -7x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -7x + x2 = 0 + 11 -7x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -7x + x2 = 11 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 = 11 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 11 + 12.25 Combine like terms: 11 + 12.25 = 23.25 12.25 + -7x + x2 = 23.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + -3.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + -3.5 = 4.82182538 Simplifying x + -3.5 = 4.82182538 Reorder the terms: -3.5 + x = 4.82182538 Solving -3.5 + x = 4.82182538 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 = 4.82182538 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.82182538 + 3.5 x = 4.82182538 + 3.5 Combine like terms: 4.82182538 + 3.5 = 8.32182538 x = 8.32182538 Simplifying x = 8.32182538Subproblem 2
x + -3.5 = -4.82182538 Simplifying x + -3.5 = -4.82182538 Reorder the terms: -3.5 + x = -4.82182538 Solving -3.5 + x = -4.82182538 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 = -4.82182538 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.82182538 + 3.5 x = -4.82182538 + 3.5 Combine like terms: -4.82182538 + 3.5 = -1.32182538 x = -1.32182538 Simplifying x = -1.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.32182538, -1.32182538}Solution
x = {8.32182538, -1.32182538}
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