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Simplifying 1463(11.8 + -1x) * x + -7.0 = 70 Reorder the terms for easier multiplication: 1463x(11.8 + -1x) + -7.0 = 70 (11.8 * 1463x + -1x * 1463x) + -7.0 = 70 (17263.4x + -1463x2) + -7.0 = 70 Reorder the terms: -7.0 + 17263.4x + -1463x2 = 70 Solving -7.0 + 17263.4x + -1463x2 = 70 Solving for variable 'x'. Reorder the terms: -7.0 + -70 + 17263.4x + -1463x2 = 70 + -70 Combine like terms: -7.0 + -70 = -77 -77 + 17263.4x + -1463x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -77 + 17263.4x + -1463x2 = 0 Begin completing the square. Divide all terms by -1463 the coefficient of the squared term: Divide each side by '-1463'. 0.05263157895 + -11.8x + x2 = 0 Move the constant term to the right: Add '-0.05263157895' to each side of the equation. 0.05263157895 + -11.8x + -0.05263157895 + x2 = 0 + -0.05263157895 Reorder the terms: 0.05263157895 + -0.05263157895 + -11.8x + x2 = 0 + -0.05263157895 Combine like terms: 0.05263157895 + -0.05263157895 = 0.00000000000 0.00000000000 + -11.8x + x2 = 0 + -0.05263157895 -11.8x + x2 = 0 + -0.05263157895 Combine like terms: 0 + -0.05263157895 = -0.05263157895 -11.8x + x2 = -0.05263157895 The x term is -11.8x. Take half its coefficient (-5.9). Square it (34.81) and add it to both sides. Add '34.81' to each side of the equation. -11.8x + 34.81 + x2 = -0.05263157895 + 34.81 Reorder the terms: 34.81 + -11.8x + x2 = -0.05263157895 + 34.81 Combine like terms: -0.05263157895 + 34.81 = 34.75736842105 34.81 + -11.8x + x2 = 34.75736842105 Factor a perfect square on the left side: (x + -5.9)(x + -5.9) = 34.75736842105 Calculate the square root of the right side: 5.895538009 Break this problem into two subproblems by setting (x + -5.9) equal to 5.895538009 and -5.895538009.Subproblem 1
x + -5.9 = 5.895538009 Simplifying x + -5.9 = 5.895538009 Reorder the terms: -5.9 + x = 5.895538009 Solving -5.9 + x = 5.895538009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.9' to each side of the equation. -5.9 + 5.9 + x = 5.895538009 + 5.9 Combine like terms: -5.9 + 5.9 = 0.0 0.0 + x = 5.895538009 + 5.9 x = 5.895538009 + 5.9 Combine like terms: 5.895538009 + 5.9 = 11.795538009 x = 11.795538009 Simplifying x = 11.795538009Subproblem 2
x + -5.9 = -5.895538009 Simplifying x + -5.9 = -5.895538009 Reorder the terms: -5.9 + x = -5.895538009 Solving -5.9 + x = -5.895538009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.9' to each side of the equation. -5.9 + 5.9 + x = -5.895538009 + 5.9 Combine like terms: -5.9 + 5.9 = 0.0 0.0 + x = -5.895538009 + 5.9 x = -5.895538009 + 5.9 Combine like terms: -5.895538009 + 5.9 = 0.004461991 x = 0.004461991 Simplifying x = 0.004461991Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.795538009, 0.004461991}
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