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Simplifying 0.8x2 + 6.4x + 15.8 = -0.8x + 4.6 Reorder the terms: 15.8 + 6.4x + 0.8x2 = -0.8x + 4.6 Reorder the terms: 15.8 + 6.4x + 0.8x2 = 4.6 + -0.8x Solving 15.8 + 6.4x + 0.8x2 = 4.6 + -0.8x Solving for variable 'x'. Reorder the terms: 15.8 + -4.6 + 6.4x + 0.8x + 0.8x2 = 4.6 + -0.8x + -4.6 + 0.8x Combine like terms: 15.8 + -4.6 = 11.2 11.2 + 6.4x + 0.8x + 0.8x2 = 4.6 + -0.8x + -4.6 + 0.8x Combine like terms: 6.4x + 0.8x = 7.2x 11.2 + 7.2x + 0.8x2 = 4.6 + -0.8x + -4.6 + 0.8x Reorder the terms: 11.2 + 7.2x + 0.8x2 = 4.6 + -4.6 + -0.8x + 0.8x Combine like terms: 4.6 + -4.6 = 0.0 11.2 + 7.2x + 0.8x2 = 0.0 + -0.8x + 0.8x 11.2 + 7.2x + 0.8x2 = -0.8x + 0.8x Combine like terms: -0.8x + 0.8x = 0.0 11.2 + 7.2x + 0.8x2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 14 + 9x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 9x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 9x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 9x + x2 = 0 + -14 9x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 9x + x2 = -14 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -14 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -14 + 20.25 Combine like terms: -14 + 20.25 = 6.25 20.25 + 9x + x2 = 6.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + 4.5) equal to 2.5 and -2.5.Subproblem 1
x + 4.5 = 2.5 Simplifying x + 4.5 = 2.5 Reorder the terms: 4.5 + x = 2.5 Solving 4.5 + x = 2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 2.5 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 2.5 + -4.5 x = 2.5 + -4.5 Combine like terms: 2.5 + -4.5 = -2 x = -2 Simplifying x = -2Subproblem 2
x + 4.5 = -2.5 Simplifying x + 4.5 = -2.5 Reorder the terms: 4.5 + x = -2.5 Solving 4.5 + x = -2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -2.5 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -2.5 + -4.5 x = -2.5 + -4.5 Combine like terms: -2.5 + -4.5 = -7 x = -7 Simplifying x = -7Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2, -7}
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