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Simplifying 42x2 + -476x + -2462 = 0 Reorder the terms: -2462 + -476x + 42x2 = 0 Solving -2462 + -476x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1231 + -238x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1231 + -238x + 21x2)' equal to zero and attempt to solve: Simplifying -1231 + -238x + 21x2 = 0 Solving -1231 + -238x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -58.61904762 + -11.33333333x + x2 = 0 Move the constant term to the right: Add '58.61904762' to each side of the equation. -58.61904762 + -11.33333333x + 58.61904762 + x2 = 0 + 58.61904762 Reorder the terms: -58.61904762 + 58.61904762 + -11.33333333x + x2 = 0 + 58.61904762 Combine like terms: -58.61904762 + 58.61904762 = 0.00000000 0.00000000 + -11.33333333x + x2 = 0 + 58.61904762 -11.33333333x + x2 = 0 + 58.61904762 Combine like terms: 0 + 58.61904762 = 58.61904762 -11.33333333x + x2 = 58.61904762 The x term is -11.33333333x. Take half its coefficient (-5.666666665). Square it (32.11111109) and add it to both sides. Add '32.11111109' to each side of the equation. -11.33333333x + 32.11111109 + x2 = 58.61904762 + 32.11111109 Reorder the terms: 32.11111109 + -11.33333333x + x2 = 58.61904762 + 32.11111109 Combine like terms: 58.61904762 + 32.11111109 = 90.73015871 32.11111109 + -11.33333333x + x2 = 90.73015871 Factor a perfect square on the left side: (x + -5.666666665)(x + -5.666666665) = 90.73015871 Calculate the square root of the right side: 9.525237987 Break this problem into two subproblems by setting (x + -5.666666665) equal to 9.525237987 and -9.525237987.Subproblem 1
x + -5.666666665 = 9.525237987 Simplifying x + -5.666666665 = 9.525237987 Reorder the terms: -5.666666665 + x = 9.525237987 Solving -5.666666665 + x = 9.525237987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = 9.525237987 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = 9.525237987 + 5.666666665 x = 9.525237987 + 5.666666665 Combine like terms: 9.525237987 + 5.666666665 = 15.191904652 x = 15.191904652 Simplifying x = 15.191904652Subproblem 2
x + -5.666666665 = -9.525237987 Simplifying x + -5.666666665 = -9.525237987 Reorder the terms: -5.666666665 + x = -9.525237987 Solving -5.666666665 + x = -9.525237987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = -9.525237987 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = -9.525237987 + 5.666666665 x = -9.525237987 + 5.666666665 Combine like terms: -9.525237987 + 5.666666665 = -3.858571322 x = -3.858571322 Simplifying x = -3.858571322Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.191904652, -3.858571322}Solution
x = {15.191904652, -3.858571322}
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