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Simplifying (69x2) + -4150x + -5300 = 0 Reorder the terms: -5300 + -4150x + (69x2) = 0 Solving -5300 + -4150x + (69x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 69 the coefficient of the squared term: Divide each side by '69'. -76.8115942 + -60.14492754x + x2 = 0 Move the constant term to the right: Add '76.8115942' to each side of the equation. -76.8115942 + -60.14492754x + 76.8115942 + x2 = 0 + 76.8115942 Reorder the terms: -76.8115942 + 76.8115942 + -60.14492754x + x2 = 0 + 76.8115942 Combine like terms: -76.8115942 + 76.8115942 = 0.0000000 0.0000000 + -60.14492754x + x2 = 0 + 76.8115942 -60.14492754x + x2 = 0 + 76.8115942 Combine like terms: 0 + 76.8115942 = 76.8115942 -60.14492754x + x2 = 76.8115942 The x term is -60.14492754x. Take half its coefficient (-30.07246377). Square it (904.3530772) and add it to both sides. Add '904.3530772' to each side of the equation. -60.14492754x + 904.3530772 + x2 = 76.8115942 + 904.3530772 Reorder the terms: 904.3530772 + -60.14492754x + x2 = 76.8115942 + 904.3530772 Combine like terms: 76.8115942 + 904.3530772 = 981.1646714 904.3530772 + -60.14492754x + x2 = 981.1646714 Factor a perfect square on the left side: ((x) + -30.07246377)((x) + -30.07246377) = 981.1646714 Calculate the square root of the right side: 31.323548193 Break this problem into two subproblems by setting ((x) + -30.07246377) equal to 31.323548193 and -31.323548193.Subproblem 1
(x) + -30.07246377 = 31.323548193 Simplifying (x) + -30.07246377 = 31.323548193 x + -30.07246377 = 31.323548193 Reorder the terms: -30.07246377 + x = 31.323548193 Solving -30.07246377 + x = 31.323548193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.07246377' to each side of the equation. -30.07246377 + 30.07246377 + x = 31.323548193 + 30.07246377 Combine like terms: -30.07246377 + 30.07246377 = 0.00000000 0.00000000 + x = 31.323548193 + 30.07246377 x = 31.323548193 + 30.07246377 Combine like terms: 31.323548193 + 30.07246377 = 61.396011963 x = 61.396011963 Simplifying x = 61.396011963Subproblem 2
(x) + -30.07246377 = -31.323548193 Simplifying (x) + -30.07246377 = -31.323548193 x + -30.07246377 = -31.323548193 Reorder the terms: -30.07246377 + x = -31.323548193 Solving -30.07246377 + x = -31.323548193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.07246377' to each side of the equation. -30.07246377 + 30.07246377 + x = -31.323548193 + 30.07246377 Combine like terms: -30.07246377 + 30.07246377 = 0.00000000 0.00000000 + x = -31.323548193 + 30.07246377 x = -31.323548193 + 30.07246377 Combine like terms: -31.323548193 + 30.07246377 = -1.251084423 x = -1.251084423 Simplifying x = -1.251084423Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.396011963, -1.251084423}
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