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Simplifying 6x2 + -4x + -99 = 0 Reorder the terms: -99 + -4x + 6x2 = 0 Solving -99 + -4x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -16.5 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + -0.6666666667x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + -0.6666666667x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + -0.6666666667x + x2 = 0 + 16.5 -0.6666666667x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 -0.6666666667x + x2 = 16.5 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 16.5 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 16.5 + 0.1111111112 Combine like terms: 16.5 + 0.1111111112 = 16.6111111112 0.1111111112 + -0.6666666667x + x2 = 16.6111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 16.6111111112 Calculate the square root of the right side: 4.075673087 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 4.075673087 and -4.075673087.Subproblem 1
x + -0.3333333334 = 4.075673087 Simplifying x + -0.3333333334 = 4.075673087 Reorder the terms: -0.3333333334 + x = 4.075673087 Solving -0.3333333334 + x = 4.075673087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 4.075673087 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 4.075673087 + 0.3333333334 x = 4.075673087 + 0.3333333334 Combine like terms: 4.075673087 + 0.3333333334 = 4.4090064204 x = 4.4090064204 Simplifying x = 4.4090064204Subproblem 2
x + -0.3333333334 = -4.075673087 Simplifying x + -0.3333333334 = -4.075673087 Reorder the terms: -0.3333333334 + x = -4.075673087 Solving -0.3333333334 + x = -4.075673087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -4.075673087 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -4.075673087 + 0.3333333334 x = -4.075673087 + 0.3333333334 Combine like terms: -4.075673087 + 0.3333333334 = -3.7423397536 x = -3.7423397536 Simplifying x = -3.7423397536Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4090064204, -3.7423397536}
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