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Simplifying 4.2x2 + -12.6x + 8.4 = x2 Reorder the terms: 8.4 + -12.6x + 4.2x2 = x2 Solving 8.4 + -12.6x + 4.2x2 = x2 Solving for variable 'x'. Combine like terms: 4.2x2 + -1x2 = 3.2x2 8.4 + -12.6x + 3.2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8.4 + -12.6x + 3.2x2 = 0 Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. 2.625 + -3.9375x + x2 = 0 Move the constant term to the right: Add '-2.625' to each side of the equation. 2.625 + -3.9375x + -2.625 + x2 = 0 + -2.625 Reorder the terms: 2.625 + -2.625 + -3.9375x + x2 = 0 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + -3.9375x + x2 = 0 + -2.625 -3.9375x + x2 = 0 + -2.625 Combine like terms: 0 + -2.625 = -2.625 -3.9375x + x2 = -2.625 The x term is -3.9375x. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375x + 3.875976563 + x2 = -2.625 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375x + x2 = -2.625 + 3.875976563 Combine like terms: -2.625 + 3.875976563 = 1.250976563 3.875976563 + -3.9375x + x2 = 1.250976563 Factor a perfect square on the left side: (x + -1.96875)(x + -1.96875) = 1.250976563 Calculate the square root of the right side: 1.118470636 Break this problem into two subproblems by setting (x + -1.96875) equal to 1.118470636 and -1.118470636.Subproblem 1
x + -1.96875 = 1.118470636 Simplifying x + -1.96875 = 1.118470636 Reorder the terms: -1.96875 + x = 1.118470636 Solving -1.96875 + x = 1.118470636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = 1.118470636 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = 1.118470636 + 1.96875 x = 1.118470636 + 1.96875 Combine like terms: 1.118470636 + 1.96875 = 3.087220636 x = 3.087220636 Simplifying x = 3.087220636Subproblem 2
x + -1.96875 = -1.118470636 Simplifying x + -1.96875 = -1.118470636 Reorder the terms: -1.96875 + x = -1.118470636 Solving -1.96875 + x = -1.118470636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = -1.118470636 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = -1.118470636 + 1.96875 x = -1.118470636 + 1.96875 Combine like terms: -1.118470636 + 1.96875 = 0.850279364 x = 0.850279364 Simplifying x = 0.850279364Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.087220636, 0.850279364}
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