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Simplifying 1.2x2 + -11x + -30 = 4x Reorder the terms: -30 + -11x + 1.2x2 = 4x Solving -30 + -11x + 1.2x2 = 4x Solving for variable 'x'. Reorder the terms: -30 + -11x + -4x + 1.2x2 = 4x + -4x Combine like terms: -11x + -4x = -15x -30 + -15x + 1.2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -30 + -15x + 1.2x2 = 0 Begin completing the square. Divide all terms by 1.2 the coefficient of the squared term: Divide each side by '1.2'. -25 + -12.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -12.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -12.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -12.5x + x2 = 0 + 25 -12.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -12.5x + x2 = 25 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 25 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 25 + 39.0625 Combine like terms: 25 + 39.0625 = 64.0625 39.0625 + -12.5x + x2 = 64.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 64.0625 Calculate the square root of the right side: 8.003905297 Break this problem into two subproblems by setting (x + -6.25) equal to 8.003905297 and -8.003905297.Subproblem 1
x + -6.25 = 8.003905297 Simplifying x + -6.25 = 8.003905297 Reorder the terms: -6.25 + x = 8.003905297 Solving -6.25 + x = 8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 8.003905297 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 8.003905297 + 6.25 x = 8.003905297 + 6.25 Combine like terms: 8.003905297 + 6.25 = 14.253905297 x = 14.253905297 Simplifying x = 14.253905297Subproblem 2
x + -6.25 = -8.003905297 Simplifying x + -6.25 = -8.003905297 Reorder the terms: -6.25 + x = -8.003905297 Solving -6.25 + x = -8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -8.003905297 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -8.003905297 + 6.25 x = -8.003905297 + 6.25 Combine like terms: -8.003905297 + 6.25 = -1.753905297 x = -1.753905297 Simplifying x = -1.753905297Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.253905297, -1.753905297}
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