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Simplifying 3.4x + 1.1x + -54.5 = 0.4x(x + -13) Reorder the terms: -54.5 + 3.4x + 1.1x = 0.4x(x + -13) Combine like terms: 3.4x + 1.1x = 4.5x -54.5 + 4.5x = 0.4x(x + -13) Reorder the terms: -54.5 + 4.5x = 0.4x(-13 + x) -54.5 + 4.5x = (-13 * 0.4x + x * 0.4x) -54.5 + 4.5x = (-5.2x + 0.4x2) Solving -54.5 + 4.5x = -5.2x + 0.4x2 Solving for variable 'x'. Combine like terms: 4.5x + 5.2x = 9.7x -54.5 + 9.7x + -0.4x2 = -5.2x + 0.4x2 + 5.2x + -0.4x2 Reorder the terms: -54.5 + 9.7x + -0.4x2 = -5.2x + 5.2x + 0.4x2 + -0.4x2 Combine like terms: -5.2x + 5.2x = 0.0 -54.5 + 9.7x + -0.4x2 = 0.0 + 0.4x2 + -0.4x2 -54.5 + 9.7x + -0.4x2 = 0.4x2 + -0.4x2 Combine like terms: 0.4x2 + -0.4x2 = 0.0 -54.5 + 9.7x + -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'. 136.25 + -24.25x + x2 = 0 Move the constant term to the right: Add '-136.25' to each side of the equation. 136.25 + -24.25x + -136.25 + x2 = 0 + -136.25 Reorder the terms: 136.25 + -136.25 + -24.25x + x2 = 0 + -136.25 Combine like terms: 136.25 + -136.25 = 0.00 0.00 + -24.25x + x2 = 0 + -136.25 -24.25x + x2 = 0 + -136.25 Combine like terms: 0 + -136.25 = -136.25 -24.25x + x2 = -136.25 The x term is -24.25x. Take half its coefficient (-12.125). Square it (147.015625) and add it to both sides. Add '147.015625' to each side of the equation. -24.25x + 147.015625 + x2 = -136.25 + 147.015625 Reorder the terms: 147.015625 + -24.25x + x2 = -136.25 + 147.015625 Combine like terms: -136.25 + 147.015625 = 10.765625 147.015625 + -24.25x + x2 = 10.765625 Factor a perfect square on the left side: (x + -12.125)(x + -12.125) = 10.765625 Calculate the square root of the right side: 3.281101187 Break this problem into two subproblems by setting (x + -12.125) equal to 3.281101187 and -3.281101187.Subproblem 1
x + -12.125 = 3.281101187 Simplifying x + -12.125 = 3.281101187 Reorder the terms: -12.125 + x = 3.281101187 Solving -12.125 + x = 3.281101187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.125' to each side of the equation. -12.125 + 12.125 + x = 3.281101187 + 12.125 Combine like terms: -12.125 + 12.125 = 0.000 0.000 + x = 3.281101187 + 12.125 x = 3.281101187 + 12.125 Combine like terms: 3.281101187 + 12.125 = 15.406101187 x = 15.406101187 Simplifying x = 15.406101187Subproblem 2
x + -12.125 = -3.281101187 Simplifying x + -12.125 = -3.281101187 Reorder the terms: -12.125 + x = -3.281101187 Solving -12.125 + x = -3.281101187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.125' to each side of the equation. -12.125 + 12.125 + x = -3.281101187 + 12.125 Combine like terms: -12.125 + 12.125 = 0.000 0.000 + x = -3.281101187 + 12.125 x = -3.281101187 + 12.125 Combine like terms: -3.281101187 + 12.125 = 8.843898813 x = 8.843898813 Simplifying x = 8.843898813Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.406101187, 8.843898813}
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