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Simplifying 2640 + 75x = 4.9x2 Solving 2640 + 75x = 4.9x2 Solving for variable 'x'. Combine like terms: 4.9x2 + -4.9x2 = 0.0 2640 + 75x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -538.7755102 + -15.30612245x + x2 = 0 Move the constant term to the right: Add '538.7755102' to each side of the equation. -538.7755102 + -15.30612245x + 538.7755102 + x2 = 0 + 538.7755102 Reorder the terms: -538.7755102 + 538.7755102 + -15.30612245x + x2 = 0 + 538.7755102 Combine like terms: -538.7755102 + 538.7755102 = 0.0000000 0.0000000 + -15.30612245x + x2 = 0 + 538.7755102 -15.30612245x + x2 = 0 + 538.7755102 Combine like terms: 0 + 538.7755102 = 538.7755102 -15.30612245x + x2 = 538.7755102 The x term is -15.30612245x. Take half its coefficient (-7.653061225). Square it (58.56934611) and add it to both sides. Add '58.56934611' to each side of the equation. -15.30612245x + 58.56934611 + x2 = 538.7755102 + 58.56934611 Reorder the terms: 58.56934611 + -15.30612245x + x2 = 538.7755102 + 58.56934611 Combine like terms: 538.7755102 + 58.56934611 = 597.34485631 58.56934611 + -15.30612245x + x2 = 597.34485631 Factor a perfect square on the left side: (x + -7.653061225)(x + -7.653061225) = 597.34485631 Calculate the square root of the right side: 24.440639442 Break this problem into two subproblems by setting (x + -7.653061225) equal to 24.440639442 and -24.440639442.Subproblem 1
x + -7.653061225 = 24.440639442 Simplifying x + -7.653061225 = 24.440639442 Reorder the terms: -7.653061225 + x = 24.440639442 Solving -7.653061225 + x = 24.440639442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.653061225' to each side of the equation. -7.653061225 + 7.653061225 + x = 24.440639442 + 7.653061225 Combine like terms: -7.653061225 + 7.653061225 = 0.000000000 0.000000000 + x = 24.440639442 + 7.653061225 x = 24.440639442 + 7.653061225 Combine like terms: 24.440639442 + 7.653061225 = 32.093700667 x = 32.093700667 Simplifying x = 32.093700667Subproblem 2
x + -7.653061225 = -24.440639442 Simplifying x + -7.653061225 = -24.440639442 Reorder the terms: -7.653061225 + x = -24.440639442 Solving -7.653061225 + x = -24.440639442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.653061225' to each side of the equation. -7.653061225 + 7.653061225 + x = -24.440639442 + 7.653061225 Combine like terms: -7.653061225 + 7.653061225 = 0.000000000 0.000000000 + x = -24.440639442 + 7.653061225 x = -24.440639442 + 7.653061225 Combine like terms: -24.440639442 + 7.653061225 = -16.787578217 x = -16.787578217 Simplifying x = -16.787578217Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.093700667, -16.787578217}
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