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Simplifying 7x2 + -2x + -100 = 0 Reorder the terms: -100 + -2x + 7x2 = 0 Solving -100 + -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'. -14.28571429 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + -0.2857142857x + 14.28571429 + x2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + -0.2857142857x + x2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + -0.2857142857x + x2 = 0 + 14.28571429 -0.2857142857x + x2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 -0.2857142857x + x2 = 14.28571429 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 = 14.28571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 14.28571429 + 0.02040816328 Combine like terms: 14.28571429 + 0.02040816328 = 14.30612245328 0.02040816328 + -0.2857142857x + x2 = 14.30612245328 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 14.30612245328 Calculate the square root of the right side: 3.782343513 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 3.782343513 and -3.782343513.Subproblem 1
x + -0.1428571429 = 3.782343513 Simplifying x + -0.1428571429 = 3.782343513 Reorder the terms: -0.1428571429 + x = 3.782343513 Solving -0.1428571429 + x = 3.782343513 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 = 3.782343513 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 3.782343513 + 0.1428571429 x = 3.782343513 + 0.1428571429 Combine like terms: 3.782343513 + 0.1428571429 = 3.9252006559 x = 3.9252006559 Simplifying x = 3.9252006559Subproblem 2
x + -0.1428571429 = -3.782343513 Simplifying x + -0.1428571429 = -3.782343513 Reorder the terms: -0.1428571429 + x = -3.782343513 Solving -0.1428571429 + x = -3.782343513 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 = -3.782343513 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -3.782343513 + 0.1428571429 x = -3.782343513 + 0.1428571429 Combine like terms: -3.782343513 + 0.1428571429 = -3.6394863701 x = -3.6394863701 Simplifying x = -3.6394863701Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9252006559, -3.6394863701}
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