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Simplifying 7x2 + -2x + -45 = 0 Reorder the terms: -45 + -2x + 7x2 = 0 Solving -45 + -2x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6.428571429 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '6.428571429' to each side of the equation. -6.428571429 + -0.2857142857x + 6.428571429 + x2 = 0 + 6.428571429 Reorder the terms: -6.428571429 + 6.428571429 + -0.2857142857x + x2 = 0 + 6.428571429 Combine like terms: -6.428571429 + 6.428571429 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0 + 6.428571429 -0.2857142857x + x2 = 0 + 6.428571429 Combine like terms: 0 + 6.428571429 = 6.428571429 -0.2857142857x + x2 = 6.428571429 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 6.428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 6.428571429 + 0.02040816328 Combine like terms: 6.428571429 + 0.02040816328 = 6.44897959228 0.02040816328 + -0.2857142857x + x2 = 6.44897959228 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 6.44897959228 Calculate the square root of the right side: 2.539484119 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 2.539484119 and -2.539484119.Subproblem 1
x + -0.1428571429 = 2.539484119 Simplifying x + -0.1428571429 = 2.539484119 Reorder the terms: -0.1428571429 + x = 2.539484119 Solving -0.1428571429 + x = 2.539484119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 2.539484119 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 2.539484119 + 0.1428571429 x = 2.539484119 + 0.1428571429 Combine like terms: 2.539484119 + 0.1428571429 = 2.6823412619 x = 2.6823412619 Simplifying x = 2.6823412619Subproblem 2
x + -0.1428571429 = -2.539484119 Simplifying x + -0.1428571429 = -2.539484119 Reorder the terms: -0.1428571429 + x = -2.539484119 Solving -0.1428571429 + x = -2.539484119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -2.539484119 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -2.539484119 + 0.1428571429 x = -2.539484119 + 0.1428571429 Combine like terms: -2.539484119 + 0.1428571429 = -2.3966269761 x = -2.3966269761 Simplifying x = -2.3966269761Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6823412619, -2.3966269761}
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