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Simplifying -0.04x2 + 2.1x + 5.4 = 0 Reorder the terms: 5.4 + 2.1x + -0.04x2 = 0 Solving 5.4 + 2.1x + -0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -135 + -52.5x + x2 = 0 Move the constant term to the right: Add '135' to each side of the equation. -135 + -52.5x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + -52.5x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -52.5x + x2 = 0 + 135 -52.5x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 -52.5x + x2 = 135 The x term is -52.5x. Take half its coefficient (-26.25). Square it (689.0625) and add it to both sides. Add '689.0625' to each side of the equation. -52.5x + 689.0625 + x2 = 135 + 689.0625 Reorder the terms: 689.0625 + -52.5x + x2 = 135 + 689.0625 Combine like terms: 135 + 689.0625 = 824.0625 689.0625 + -52.5x + x2 = 824.0625 Factor a perfect square on the left side: (x + -26.25)(x + -26.25) = 824.0625 Calculate the square root of the right side: 28.706488814 Break this problem into two subproblems by setting (x + -26.25) equal to 28.706488814 and -28.706488814.Subproblem 1
x + -26.25 = 28.706488814 Simplifying x + -26.25 = 28.706488814 Reorder the terms: -26.25 + x = 28.706488814 Solving -26.25 + x = 28.706488814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.25' to each side of the equation. -26.25 + 26.25 + x = 28.706488814 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + x = 28.706488814 + 26.25 x = 28.706488814 + 26.25 Combine like terms: 28.706488814 + 26.25 = 54.956488814 x = 54.956488814 Simplifying x = 54.956488814Subproblem 2
x + -26.25 = -28.706488814 Simplifying x + -26.25 = -28.706488814 Reorder the terms: -26.25 + x = -28.706488814 Solving -26.25 + x = -28.706488814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.25' to each side of the equation. -26.25 + 26.25 + x = -28.706488814 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + x = -28.706488814 + 26.25 x = -28.706488814 + 26.25 Combine like terms: -28.706488814 + 26.25 = -2.456488814 x = -2.456488814 Simplifying x = -2.456488814Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.956488814, -2.456488814}
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