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Simplifying 0 = 0.4x2 + 0.8x + -48 Reorder the terms: 0 = -48 + 0.8x + 0.4x2 Solving 0 = -48 + 0.8x + 0.4x2 Solving for variable 'x'. Combine like terms: 0 + 48 = 48 48 + -0.8x + -0.4x2 = -48 + 0.8x + 0.4x2 + 48 + -0.8x + -0.4x2 Reorder the terms: 48 + -0.8x + -0.4x2 = -48 + 48 + 0.8x + -0.8x + 0.4x2 + -0.4x2 Combine like terms: -48 + 48 = 0 48 + -0.8x + -0.4x2 = 0 + 0.8x + -0.8x + 0.4x2 + -0.4x2 48 + -0.8x + -0.4x2 = 0.8x + -0.8x + 0.4x2 + -0.4x2 Combine like terms: 0.8x + -0.8x = 0.0 48 + -0.8x + -0.4x2 = 0.0 + 0.4x2 + -0.4x2 48 + -0.8x + -0.4x2 = 0.4x2 + -0.4x2 Combine like terms: 0.4x2 + -0.4x2 = 0.0 48 + -0.8x + -0.4x2 = 0.0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -120 + 2x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 2x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 2x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 2x + x2 = 0 + 120 2x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 2x + x2 = 120 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 120 + 1 Reorder the terms: 1 + 2x + x2 = 120 + 1 Combine like terms: 120 + 1 = 121 1 + 2x + x2 = 121 Factor a perfect square on the left side: (x + 1)(x + 1) = 121 Calculate the square root of the right side: 11 Break this problem into two subproblems by setting (x + 1) equal to 11 and -11.Subproblem 1
x + 1 = 11 Simplifying x + 1 = 11 Reorder the terms: 1 + x = 11 Solving 1 + x = 11 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 11 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11 + -1 x = 11 + -1 Combine like terms: 11 + -1 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 1 = -11 Simplifying x + 1 = -11 Reorder the terms: 1 + x = -11 Solving 1 + x = -11 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -11 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11 + -1 x = -11 + -1 Combine like terms: -11 + -1 = -12 x = -12 Simplifying x = -12Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -12}
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