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Simplifying 49x2 + -84x = 307 Reorder the terms: -84x + 49x2 = 307 Solving -84x + 49x2 = 307 Solving for variable 'x'. Reorder the terms: -307 + -84x + 49x2 = 307 + -307 Combine like terms: 307 + -307 = 0 -307 + -84x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -6.265306122 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '6.265306122' to each side of the equation. -6.265306122 + -1.714285714x + 6.265306122 + x2 = 0 + 6.265306122 Reorder the terms: -6.265306122 + 6.265306122 + -1.714285714x + x2 = 0 + 6.265306122 Combine like terms: -6.265306122 + 6.265306122 = 0.000000000 0.000000000 + -1.714285714x + x2 = 0 + 6.265306122 -1.714285714x + x2 = 0 + 6.265306122 Combine like terms: 0 + 6.265306122 = 6.265306122 -1.714285714x + x2 = 6.265306122 The x term is -1.714285714x. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714x + 0.7346938773 + x2 = 6.265306122 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = 6.265306122 + 0.7346938773 Combine like terms: 6.265306122 + 0.7346938773 = 6.9999999993 0.7346938773 + -1.714285714x + x2 = 6.9999999993 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 6.9999999993 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -0.857142857) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -0.857142857 = 2.645751311 Simplifying x + -0.857142857 = 2.645751311 Reorder the terms: -0.857142857 + x = 2.645751311 Solving -0.857142857 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 2.645751311 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 2.645751311 + 0.857142857 x = 2.645751311 + 0.857142857 Combine like terms: 2.645751311 + 0.857142857 = 3.502894168 x = 3.502894168 Simplifying x = 3.502894168Subproblem 2
x + -0.857142857 = -2.645751311 Simplifying x + -0.857142857 = -2.645751311 Reorder the terms: -0.857142857 + x = -2.645751311 Solving -0.857142857 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -2.645751311 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -2.645751311 + 0.857142857 x = -2.645751311 + 0.857142857 Combine like terms: -2.645751311 + 0.857142857 = -1.788608454 x = -1.788608454 Simplifying x = -1.788608454Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.502894168, -1.788608454}
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