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Simplifying 4x2 + -69x + 20 = 7x2 + -8 Reorder the terms: 20 + -69x + 4x2 = 7x2 + -8 Reorder the terms: 20 + -69x + 4x2 = -8 + 7x2 Solving 20 + -69x + 4x2 = -8 + 7x2 Solving for variable 'x'. Reorder the terms: 20 + 8 + -69x + 4x2 + -7x2 = -8 + 7x2 + 8 + -7x2 Combine like terms: 20 + 8 = 28 28 + -69x + 4x2 + -7x2 = -8 + 7x2 + 8 + -7x2 Combine like terms: 4x2 + -7x2 = -3x2 28 + -69x + -3x2 = -8 + 7x2 + 8 + -7x2 Reorder the terms: 28 + -69x + -3x2 = -8 + 8 + 7x2 + -7x2 Combine like terms: -8 + 8 = 0 28 + -69x + -3x2 = 0 + 7x2 + -7x2 28 + -69x + -3x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 28 + -69x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -9.333333333 + 23x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + 23x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + 23x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + 23x + x2 = 0 + 9.333333333 23x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 23x + x2 = 9.333333333 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 9.333333333 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 9.333333333 + 132.25 Combine like terms: 9.333333333 + 132.25 = 141.583333333 132.25 + 23x + x2 = 141.583333333 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 141.583333333 Calculate the square root of the right side: 11.898879499 Break this problem into two subproblems by setting (x + 11.5) equal to 11.898879499 and -11.898879499.Subproblem 1
x + 11.5 = 11.898879499 Simplifying x + 11.5 = 11.898879499 Reorder the terms: 11.5 + x = 11.898879499 Solving 11.5 + x = 11.898879499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 11.898879499 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 11.898879499 + -11.5 x = 11.898879499 + -11.5 Combine like terms: 11.898879499 + -11.5 = 0.398879499 x = 0.398879499 Simplifying x = 0.398879499Subproblem 2
x + 11.5 = -11.898879499 Simplifying x + 11.5 = -11.898879499 Reorder the terms: 11.5 + x = -11.898879499 Solving 11.5 + x = -11.898879499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -11.898879499 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -11.898879499 + -11.5 x = -11.898879499 + -11.5 Combine like terms: -11.898879499 + -11.5 = -23.398879499 x = -23.398879499 Simplifying x = -23.398879499Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.398879499, -23.398879499}
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