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Simplifying 25 = -0.04x2 + 2.1x + 6.1 Reorder the terms: 25 = 6.1 + 2.1x + -0.04x2 Solving 25 = 6.1 + 2.1x + -0.04x2 Solving for variable 'x'. Combine like terms: 25 + -6.1 = 18.9 18.9 + -2.1x + 0.04x2 = 6.1 + 2.1x + -0.04x2 + -6.1 + -2.1x + 0.04x2 Reorder the terms: 18.9 + -2.1x + 0.04x2 = 6.1 + -6.1 + 2.1x + -2.1x + -0.04x2 + 0.04x2 Combine like terms: 6.1 + -6.1 = 0.0 18.9 + -2.1x + 0.04x2 = 0.0 + 2.1x + -2.1x + -0.04x2 + 0.04x2 18.9 + -2.1x + 0.04x2 = 2.1x + -2.1x + -0.04x2 + 0.04x2 Combine like terms: 2.1x + -2.1x = 0.0 18.9 + -2.1x + 0.04x2 = 0.0 + -0.04x2 + 0.04x2 18.9 + -2.1x + 0.04x2 = -0.04x2 + 0.04x2 Combine like terms: -0.04x2 + 0.04x2 = 0.00 18.9 + -2.1x + 0.04x2 = 0.00 Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 472.5 + -52.5x + x2 = 0 Move the constant term to the right: Add '-472.5' to each side of the equation. 472.5 + -52.5x + -472.5 + x2 = 0 + -472.5 Reorder the terms: 472.5 + -472.5 + -52.5x + x2 = 0 + -472.5 Combine like terms: 472.5 + -472.5 = 0.0 0.0 + -52.5x + x2 = 0 + -472.5 -52.5x + x2 = 0 + -472.5 Combine like terms: 0 + -472.5 = -472.5 -52.5x + x2 = -472.5 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 = -472.5 + 689.0625 Reorder the terms: 689.0625 + -52.5x + x2 = -472.5 + 689.0625 Combine like terms: -472.5 + 689.0625 = 216.5625 689.0625 + -52.5x + x2 = 216.5625 Factor a perfect square on the left side: (x + -26.25)(x + -26.25) = 216.5625 Calculate the square root of the right side: 14.716062653 Break this problem into two subproblems by setting (x + -26.25) equal to 14.716062653 and -14.716062653.Subproblem 1
x + -26.25 = 14.716062653 Simplifying x + -26.25 = 14.716062653 Reorder the terms: -26.25 + x = 14.716062653 Solving -26.25 + x = 14.716062653 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 = 14.716062653 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + x = 14.716062653 + 26.25 x = 14.716062653 + 26.25 Combine like terms: 14.716062653 + 26.25 = 40.966062653 x = 40.966062653 Simplifying x = 40.966062653Subproblem 2
x + -26.25 = -14.716062653 Simplifying x + -26.25 = -14.716062653 Reorder the terms: -26.25 + x = -14.716062653 Solving -26.25 + x = -14.716062653 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 = -14.716062653 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + x = -14.716062653 + 26.25 x = -14.716062653 + 26.25 Combine like terms: -14.716062653 + 26.25 = 11.533937347 x = 11.533937347 Simplifying x = 11.533937347Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.966062653, 11.533937347}
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