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Simplifying 63x2 + 44x + -5 = 0 Reorder the terms: -5 + 44x + 63x2 = 0 Solving -5 + 44x + 63x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -0.07936507937 + 0.6984126984x + x2 = 0 Move the constant term to the right: Add '0.07936507937' to each side of the equation. -0.07936507937 + 0.6984126984x + 0.07936507937 + x2 = 0 + 0.07936507937 Reorder the terms: -0.07936507937 + 0.07936507937 + 0.6984126984x + x2 = 0 + 0.07936507937 Combine like terms: -0.07936507937 + 0.07936507937 = 0.00000000000 0.00000000000 + 0.6984126984x + x2 = 0 + 0.07936507937 0.6984126984x + x2 = 0 + 0.07936507937 Combine like terms: 0 + 0.07936507937 = 0.07936507937 0.6984126984x + x2 = 0.07936507937 The x term is 0.6984126984x. Take half its coefficient (0.3492063492). Square it (0.1219450743) and add it to both sides. Add '0.1219450743' to each side of the equation. 0.6984126984x + 0.1219450743 + x2 = 0.07936507937 + 0.1219450743 Reorder the terms: 0.1219450743 + 0.6984126984x + x2 = 0.07936507937 + 0.1219450743 Combine like terms: 0.07936507937 + 0.1219450743 = 0.20131015367 0.1219450743 + 0.6984126984x + x2 = 0.20131015367 Factor a perfect square on the left side: (x + 0.3492063492)(x + 0.3492063492) = 0.20131015367 Calculate the square root of the right side: 0.448676001 Break this problem into two subproblems by setting (x + 0.3492063492) equal to 0.448676001 and -0.448676001.Subproblem 1
x + 0.3492063492 = 0.448676001 Simplifying x + 0.3492063492 = 0.448676001 Reorder the terms: 0.3492063492 + x = 0.448676001 Solving 0.3492063492 + x = 0.448676001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3492063492' to each side of the equation. 0.3492063492 + -0.3492063492 + x = 0.448676001 + -0.3492063492 Combine like terms: 0.3492063492 + -0.3492063492 = 0.0000000000 0.0000000000 + x = 0.448676001 + -0.3492063492 x = 0.448676001 + -0.3492063492 Combine like terms: 0.448676001 + -0.3492063492 = 0.0994696518 x = 0.0994696518 Simplifying x = 0.0994696518Subproblem 2
x + 0.3492063492 = -0.448676001 Simplifying x + 0.3492063492 = -0.448676001 Reorder the terms: 0.3492063492 + x = -0.448676001 Solving 0.3492063492 + x = -0.448676001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3492063492' to each side of the equation. 0.3492063492 + -0.3492063492 + x = -0.448676001 + -0.3492063492 Combine like terms: 0.3492063492 + -0.3492063492 = 0.0000000000 0.0000000000 + x = -0.448676001 + -0.3492063492 x = -0.448676001 + -0.3492063492 Combine like terms: -0.448676001 + -0.3492063492 = -0.7978823502 x = -0.7978823502 Simplifying x = -0.7978823502Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0994696518, -0.7978823502}
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