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Simplifying 21x2 + 74x + -88 = 0 Reorder the terms: -88 + 74x + 21x2 = 0 Solving -88 + 74x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -4.19047619 + 3.523809524x + x2 = 0 Move the constant term to the right: Add '4.19047619' to each side of the equation. -4.19047619 + 3.523809524x + 4.19047619 + x2 = 0 + 4.19047619 Reorder the terms: -4.19047619 + 4.19047619 + 3.523809524x + x2 = 0 + 4.19047619 Combine like terms: -4.19047619 + 4.19047619 = 0.00000000 0.00000000 + 3.523809524x + x2 = 0 + 4.19047619 3.523809524x + x2 = 0 + 4.19047619 Combine like terms: 0 + 4.19047619 = 4.19047619 3.523809524x + x2 = 4.19047619 The x term is 3.523809524x. Take half its coefficient (1.761904762). Square it (3.104308390) and add it to both sides. Add '3.104308390' to each side of the equation. 3.523809524x + 3.104308390 + x2 = 4.19047619 + 3.104308390 Reorder the terms: 3.104308390 + 3.523809524x + x2 = 4.19047619 + 3.104308390 Combine like terms: 4.19047619 + 3.104308390 = 7.29478458 3.104308390 + 3.523809524x + x2 = 7.29478458 Factor a perfect square on the left side: (x + 1.761904762)(x + 1.761904762) = 7.29478458 Calculate the square root of the right side: 2.700885888 Break this problem into two subproblems by setting (x + 1.761904762) equal to 2.700885888 and -2.700885888.Subproblem 1
x + 1.761904762 = 2.700885888 Simplifying x + 1.761904762 = 2.700885888 Reorder the terms: 1.761904762 + x = 2.700885888 Solving 1.761904762 + x = 2.700885888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.761904762' to each side of the equation. 1.761904762 + -1.761904762 + x = 2.700885888 + -1.761904762 Combine like terms: 1.761904762 + -1.761904762 = 0.000000000 0.000000000 + x = 2.700885888 + -1.761904762 x = 2.700885888 + -1.761904762 Combine like terms: 2.700885888 + -1.761904762 = 0.938981126 x = 0.938981126 Simplifying x = 0.938981126Subproblem 2
x + 1.761904762 = -2.700885888 Simplifying x + 1.761904762 = -2.700885888 Reorder the terms: 1.761904762 + x = -2.700885888 Solving 1.761904762 + x = -2.700885888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.761904762' to each side of the equation. 1.761904762 + -1.761904762 + x = -2.700885888 + -1.761904762 Combine like terms: 1.761904762 + -1.761904762 = 0.000000000 0.000000000 + x = -2.700885888 + -1.761904762 x = -2.700885888 + -1.761904762 Combine like terms: -2.700885888 + -1.761904762 = -4.46279065 x = -4.46279065 Simplifying x = -4.46279065Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.938981126, -4.46279065}
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