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Simplifying 2 + -1(x + 2)(x + -2) = 3x + -15 Reorder the terms: 2 + -1(2 + x)(x + -2) = 3x + -15 Reorder the terms: 2 + -1(2 + x)(-2 + x) = 3x + -15 Multiply (2 + x) * (-2 + x) 2 + -1(2(-2 + x) + x(-2 + x)) = 3x + -15 2 + -1((-2 * 2 + x * 2) + x(-2 + x)) = 3x + -15 2 + -1((-4 + 2x) + x(-2 + x)) = 3x + -15 2 + -1(-4 + 2x + (-2 * x + x * x)) = 3x + -15 2 + -1(-4 + 2x + (-2x + x2)) = 3x + -15 Combine like terms: 2x + -2x = 0 2 + -1(-4 + 0 + x2) = 3x + -15 2 + -1(-4 + x2) = 3x + -15 2 + (-4 * -1 + x2 * -1) = 3x + -15 2 + (4 + -1x2) = 3x + -15 Combine like terms: 2 + 4 = 6 6 + -1x2 = 3x + -15 Reorder the terms: 6 + -1x2 = -15 + 3x Solving 6 + -1x2 = -15 + 3x Solving for variable 'x'. Reorder the terms: 6 + 15 + -3x + -1x2 = -15 + 3x + 15 + -3x Combine like terms: 6 + 15 = 21 21 + -3x + -1x2 = -15 + 3x + 15 + -3x Reorder the terms: 21 + -3x + -1x2 = -15 + 15 + 3x + -3x Combine like terms: -15 + 15 = 0 21 + -3x + -1x2 = 0 + 3x + -3x 21 + -3x + -1x2 = 3x + -3x Combine like terms: 3x + -3x = 0 21 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + 3x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 3x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 3x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 3x + x2 = 0 + 21 3x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 3x + x2 = 21 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 21 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 21 + 2.25 Combine like terms: 21 + 2.25 = 23.25 2.25 + 3x + x2 = 23.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + 1.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + 1.5 = 4.82182538 Simplifying x + 1.5 = 4.82182538 Reorder the terms: 1.5 + x = 4.82182538 Solving 1.5 + x = 4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.82182538 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.82182538 + -1.5 x = 4.82182538 + -1.5 Combine like terms: 4.82182538 + -1.5 = 3.32182538 x = 3.32182538 Simplifying x = 3.32182538Subproblem 2
x + 1.5 = -4.82182538 Simplifying x + 1.5 = -4.82182538 Reorder the terms: 1.5 + x = -4.82182538 Solving 1.5 + x = -4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.82182538 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.82182538 + -1.5 x = -4.82182538 + -1.5 Combine like terms: -4.82182538 + -1.5 = -6.32182538 x = -6.32182538 Simplifying x = -6.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.32182538, -6.32182538}
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