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Simplifying 19x2 + -14x + -148.25 = 0 Reorder the terms: -148.25 + -14x + 19x2 = 0 Solving -148.25 + -14x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -7.802631579 + -0.7368421053x + x2 = 0 Move the constant term to the right: Add '7.802631579' to each side of the equation. -7.802631579 + -0.7368421053x + 7.802631579 + x2 = 0 + 7.802631579 Reorder the terms: -7.802631579 + 7.802631579 + -0.7368421053x + x2 = 0 + 7.802631579 Combine like terms: -7.802631579 + 7.802631579 = 0.000000000 0.000000000 + -0.7368421053x + x2 = 0 + 7.802631579 -0.7368421053x + x2 = 0 + 7.802631579 Combine like terms: 0 + 7.802631579 = 7.802631579 -0.7368421053x + x2 = 7.802631579 The x term is -0.7368421053x. Take half its coefficient (-0.3684210527). Square it (0.1357340721) and add it to both sides. Add '0.1357340721' to each side of the equation. -0.7368421053x + 0.1357340721 + x2 = 7.802631579 + 0.1357340721 Reorder the terms: 0.1357340721 + -0.7368421053x + x2 = 7.802631579 + 0.1357340721 Combine like terms: 7.802631579 + 0.1357340721 = 7.9383656511 0.1357340721 + -0.7368421053x + x2 = 7.9383656511 Factor a perfect square on the left side: (x + -0.3684210527)(x + -0.3684210527) = 7.9383656511 Calculate the square root of the right side: 2.817510541 Break this problem into two subproblems by setting (x + -0.3684210527) equal to 2.817510541 and -2.817510541.Subproblem 1
x + -0.3684210527 = 2.817510541 Simplifying x + -0.3684210527 = 2.817510541 Reorder the terms: -0.3684210527 + x = 2.817510541 Solving -0.3684210527 + x = 2.817510541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3684210527' to each side of the equation. -0.3684210527 + 0.3684210527 + x = 2.817510541 + 0.3684210527 Combine like terms: -0.3684210527 + 0.3684210527 = 0.0000000000 0.0000000000 + x = 2.817510541 + 0.3684210527 x = 2.817510541 + 0.3684210527 Combine like terms: 2.817510541 + 0.3684210527 = 3.1859315937 x = 3.1859315937 Simplifying x = 3.1859315937Subproblem 2
x + -0.3684210527 = -2.817510541 Simplifying x + -0.3684210527 = -2.817510541 Reorder the terms: -0.3684210527 + x = -2.817510541 Solving -0.3684210527 + x = -2.817510541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3684210527' to each side of the equation. -0.3684210527 + 0.3684210527 + x = -2.817510541 + 0.3684210527 Combine like terms: -0.3684210527 + 0.3684210527 = 0.0000000000 0.0000000000 + x = -2.817510541 + 0.3684210527 x = -2.817510541 + 0.3684210527 Combine like terms: -2.817510541 + 0.3684210527 = -2.4490894883 x = -2.4490894883 Simplifying x = -2.4490894883Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1859315937, -2.4490894883}
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