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Simplifying -0.004x2 + 1.15x + 12 = 0 Reorder the terms: 12 + 1.15x + -0.004x2 = 0 Solving 12 + 1.15x + -0.004x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.004 the coefficient of the squared term: Divide each side by '-0.004'. -3000 + -287.5x + x2 = 0 Move the constant term to the right: Add '3000' to each side of the equation. -3000 + -287.5x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + -287.5x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + -287.5x + x2 = 0 + 3000 -287.5x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 -287.5x + x2 = 3000 The x term is -287.5x. Take half its coefficient (-143.75). Square it (20664.0625) and add it to both sides. Add '20664.0625' to each side of the equation. -287.5x + 20664.0625 + x2 = 3000 + 20664.0625 Reorder the terms: 20664.0625 + -287.5x + x2 = 3000 + 20664.0625 Combine like terms: 3000 + 20664.0625 = 23664.0625 20664.0625 + -287.5x + x2 = 23664.0625 Factor a perfect square on the left side: (x + -143.75)(x + -143.75) = 23664.0625 Calculate the square root of the right side: 153.831279329 Break this problem into two subproblems by setting (x + -143.75) equal to 153.831279329 and -153.831279329.Subproblem 1
x + -143.75 = 153.831279329 Simplifying x + -143.75 = 153.831279329 Reorder the terms: -143.75 + x = 153.831279329 Solving -143.75 + x = 153.831279329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '143.75' to each side of the equation. -143.75 + 143.75 + x = 153.831279329 + 143.75 Combine like terms: -143.75 + 143.75 = 0.00 0.00 + x = 153.831279329 + 143.75 x = 153.831279329 + 143.75 Combine like terms: 153.831279329 + 143.75 = 297.581279329 x = 297.581279329 Simplifying x = 297.581279329Subproblem 2
x + -143.75 = -153.831279329 Simplifying x + -143.75 = -153.831279329 Reorder the terms: -143.75 + x = -153.831279329 Solving -143.75 + x = -153.831279329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '143.75' to each side of the equation. -143.75 + 143.75 + x = -153.831279329 + 143.75 Combine like terms: -143.75 + 143.75 = 0.00 0.00 + x = -153.831279329 + 143.75 x = -153.831279329 + 143.75 Combine like terms: -153.831279329 + 143.75 = -10.081279329 x = -10.081279329 Simplifying x = -10.081279329Solution
The solution to the problem is based on the solutions from the subproblems. x = {297.581279329, -10.081279329}
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