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Simplifying 9x + 4.9x2 + -750 = 0 Reorder the terms: -750 + 9x + 4.9x2 = 0 Solving -750 + 9x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -153.0612245 + 1.836734694x + x2 = 0 Move the constant term to the right: Add '153.0612245' to each side of the equation. -153.0612245 + 1.836734694x + 153.0612245 + x2 = 0 + 153.0612245 Reorder the terms: -153.0612245 + 153.0612245 + 1.836734694x + x2 = 0 + 153.0612245 Combine like terms: -153.0612245 + 153.0612245 = 0.0000000 0.0000000 + 1.836734694x + x2 = 0 + 153.0612245 1.836734694x + x2 = 0 + 153.0612245 Combine like terms: 0 + 153.0612245 = 153.0612245 1.836734694x + x2 = 153.0612245 The x term is 1.836734694x. Take half its coefficient (0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. 1.836734694x + 0.8433985840 + x2 = 153.0612245 + 0.8433985840 Reorder the terms: 0.8433985840 + 1.836734694x + x2 = 153.0612245 + 0.8433985840 Combine like terms: 153.0612245 + 0.8433985840 = 153.904623084 0.8433985840 + 1.836734694x + x2 = 153.904623084 Factor a perfect square on the left side: (x + 0.918367347)(x + 0.918367347) = 153.904623084 Calculate the square root of the right side: 12.405830205 Break this problem into two subproblems by setting (x + 0.918367347) equal to 12.405830205 and -12.405830205.Subproblem 1
x + 0.918367347 = 12.405830205 Simplifying x + 0.918367347 = 12.405830205 Reorder the terms: 0.918367347 + x = 12.405830205 Solving 0.918367347 + x = 12.405830205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.918367347' to each side of the equation. 0.918367347 + -0.918367347 + x = 12.405830205 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + x = 12.405830205 + -0.918367347 x = 12.405830205 + -0.918367347 Combine like terms: 12.405830205 + -0.918367347 = 11.487462858 x = 11.487462858 Simplifying x = 11.487462858Subproblem 2
x + 0.918367347 = -12.405830205 Simplifying x + 0.918367347 = -12.405830205 Reorder the terms: 0.918367347 + x = -12.405830205 Solving 0.918367347 + x = -12.405830205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.918367347' to each side of the equation. 0.918367347 + -0.918367347 + x = -12.405830205 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + x = -12.405830205 + -0.918367347 x = -12.405830205 + -0.918367347 Combine like terms: -12.405830205 + -0.918367347 = -13.324197552 x = -13.324197552 Simplifying x = -13.324197552Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.487462858, -13.324197552}
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