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Simplifying 185322 = 0.6213x2 + 468.84x + 14091 Reorder the terms: 185322 = 14091 + 468.84x + 0.6213x2 Solving 185322 = 14091 + 468.84x + 0.6213x2 Solving for variable 'x'. Combine like terms: 185322 + -14091 = 171231 171231 + -468.84x + -0.6213x2 = 14091 + 468.84x + 0.6213x2 + -14091 + -468.84x + -0.6213x2 Reorder the terms: 171231 + -468.84x + -0.6213x2 = 14091 + -14091 + 468.84x + -468.84x + 0.6213x2 + -0.6213x2 Combine like terms: 14091 + -14091 = 0 171231 + -468.84x + -0.6213x2 = 0 + 468.84x + -468.84x + 0.6213x2 + -0.6213x2 171231 + -468.84x + -0.6213x2 = 468.84x + -468.84x + 0.6213x2 + -0.6213x2 Combine like terms: 468.84x + -468.84x = 0.00 171231 + -468.84x + -0.6213x2 = 0.00 + 0.6213x2 + -0.6213x2 171231 + -468.84x + -0.6213x2 = 0.6213x2 + -0.6213x2 Combine like terms: 0.6213x2 + -0.6213x2 = 0.0000 171231 + -468.84x + -0.6213x2 = 0.0000 Begin completing the square. Divide all terms by -0.6213 the coefficient of the squared term: Divide each side by '-0.6213'. -275601.1589 + 754.6112989x + x2 = 0 Move the constant term to the right: Add '275601.1589' to each side of the equation. -275601.1589 + 754.6112989x + 275601.1589 + x2 = 0 + 275601.1589 Reorder the terms: -275601.1589 + 275601.1589 + 754.6112989x + x2 = 0 + 275601.1589 Combine like terms: -275601.1589 + 275601.1589 = 0.0000 0.0000 + 754.6112989x + x2 = 0 + 275601.1589 754.6112989x + x2 = 0 + 275601.1589 Combine like terms: 0 + 275601.1589 = 275601.1589 754.6112989x + x2 = 275601.1589 The x term is 754.6112989x. Take half its coefficient (377.3056495). Square it (142359.5531) and add it to both sides. Add '142359.5531' to each side of the equation. 754.6112989x + 142359.5531 + x2 = 275601.1589 + 142359.5531 Reorder the terms: 142359.5531 + 754.6112989x + x2 = 275601.1589 + 142359.5531 Combine like terms: 275601.1589 + 142359.5531 = 417960.712 142359.5531 + 754.6112989x + x2 = 417960.712 Factor a perfect square on the left side: (x + 377.3056495)(x + 377.3056495) = 417960.712 Calculate the square root of the right side: 646.498810517 Break this problem into two subproblems by setting (x + 377.3056495) equal to 646.498810517 and -646.498810517.Subproblem 1
x + 377.3056495 = 646.498810517 Simplifying x + 377.3056495 = 646.498810517 Reorder the terms: 377.3056495 + x = 646.498810517 Solving 377.3056495 + x = 646.498810517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-377.3056495' to each side of the equation. 377.3056495 + -377.3056495 + x = 646.498810517 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = 646.498810517 + -377.3056495 x = 646.498810517 + -377.3056495 Combine like terms: 646.498810517 + -377.3056495 = 269.193161017 x = 269.193161017 Simplifying x = 269.193161017Subproblem 2
x + 377.3056495 = -646.498810517 Simplifying x + 377.3056495 = -646.498810517 Reorder the terms: 377.3056495 + x = -646.498810517 Solving 377.3056495 + x = -646.498810517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-377.3056495' to each side of the equation. 377.3056495 + -377.3056495 + x = -646.498810517 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = -646.498810517 + -377.3056495 x = -646.498810517 + -377.3056495 Combine like terms: -646.498810517 + -377.3056495 = -1023.804460017 x = -1023.804460017 Simplifying x = -1023.804460017Solution
The solution to the problem is based on the solutions from the subproblems. x = {269.193161017, -1023.804460017}
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