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Simplifying 0 = -1.5x2 + 12x + -20.5 Reorder the terms: 0 = -20.5 + 12x + -1.5x2 Solving 0 = -20.5 + 12x + -1.5x2 Solving for variable 'x'. Combine like terms: 0 + 20.5 = 20.5 20.5 + -12x + 1.5x2 = -20.5 + 12x + -1.5x2 + 20.5 + -12x + 1.5x2 Reorder the terms: 20.5 + -12x + 1.5x2 = -20.5 + 20.5 + 12x + -12x + -1.5x2 + 1.5x2 Combine like terms: -20.5 + 20.5 = 0.0 20.5 + -12x + 1.5x2 = 0.0 + 12x + -12x + -1.5x2 + 1.5x2 20.5 + -12x + 1.5x2 = 12x + -12x + -1.5x2 + 1.5x2 Combine like terms: 12x + -12x = 0 20.5 + -12x + 1.5x2 = 0 + -1.5x2 + 1.5x2 20.5 + -12x + 1.5x2 = -1.5x2 + 1.5x2 Combine like terms: -1.5x2 + 1.5x2 = 0.0 20.5 + -12x + 1.5x2 = 0.0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 13.66666667 + -8x + x2 = 0 Move the constant term to the right: Add '-13.66666667' to each side of the equation. 13.66666667 + -8x + -13.66666667 + x2 = 0 + -13.66666667 Reorder the terms: 13.66666667 + -13.66666667 + -8x + x2 = 0 + -13.66666667 Combine like terms: 13.66666667 + -13.66666667 = 0.00000000 0.00000000 + -8x + x2 = 0 + -13.66666667 -8x + x2 = 0 + -13.66666667 Combine like terms: 0 + -13.66666667 = -13.66666667 -8x + x2 = -13.66666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -13.66666667 + 16 Reorder the terms: 16 + -8x + x2 = -13.66666667 + 16 Combine like terms: -13.66666667 + 16 = 2.33333333 16 + -8x + x2 = 2.33333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 2.33333333 Calculate the square root of the right side: 1.527525231 Break this problem into two subproblems by setting (x + -4) equal to 1.527525231 and -1.527525231.Subproblem 1
x + -4 = 1.527525231 Simplifying x + -4 = 1.527525231 Reorder the terms: -4 + x = 1.527525231 Solving -4 + x = 1.527525231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 1.527525231 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.527525231 + 4 x = 1.527525231 + 4 Combine like terms: 1.527525231 + 4 = 5.527525231 x = 5.527525231 Simplifying x = 5.527525231Subproblem 2
x + -4 = -1.527525231 Simplifying x + -4 = -1.527525231 Reorder the terms: -4 + x = -1.527525231 Solving -4 + x = -1.527525231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -1.527525231 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.527525231 + 4 x = -1.527525231 + 4 Combine like terms: -1.527525231 + 4 = 2.472474769 x = 2.472474769 Simplifying x = 2.472474769Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.527525231, 2.472474769}
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