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Simplifying 3x2 + -88x + -18 = 0 Reorder the terms: -18 + -88x + 3x2 = 0 Solving -18 + -88x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -29.33333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -29.33333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -29.33333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -29.33333333x + x2 = 0 + 6 -29.33333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -29.33333333x + x2 = 6 The x term is -29.33333333x. Take half its coefficient (-14.66666667). Square it (215.1111112) and add it to both sides. Add '215.1111112' to each side of the equation. -29.33333333x + 215.1111112 + x2 = 6 + 215.1111112 Reorder the terms: 215.1111112 + -29.33333333x + x2 = 6 + 215.1111112 Combine like terms: 6 + 215.1111112 = 221.1111112 215.1111112 + -29.33333333x + x2 = 221.1111112 Factor a perfect square on the left side: (x + -14.66666667)(x + -14.66666667) = 221.1111112 Calculate the square root of the right side: 14.869805352 Break this problem into two subproblems by setting (x + -14.66666667) equal to 14.869805352 and -14.869805352.Subproblem 1
x + -14.66666667 = 14.869805352 Simplifying x + -14.66666667 = 14.869805352 Reorder the terms: -14.66666667 + x = 14.869805352 Solving -14.66666667 + x = 14.869805352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.66666667' to each side of the equation. -14.66666667 + 14.66666667 + x = 14.869805352 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + x = 14.869805352 + 14.66666667 x = 14.869805352 + 14.66666667 Combine like terms: 14.869805352 + 14.66666667 = 29.536472022 x = 29.536472022 Simplifying x = 29.536472022Subproblem 2
x + -14.66666667 = -14.869805352 Simplifying x + -14.66666667 = -14.869805352 Reorder the terms: -14.66666667 + x = -14.869805352 Solving -14.66666667 + x = -14.869805352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.66666667' to each side of the equation. -14.66666667 + 14.66666667 + x = -14.869805352 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + x = -14.869805352 + 14.66666667 x = -14.869805352 + 14.66666667 Combine like terms: -14.869805352 + 14.66666667 = -0.203138682 x = -0.203138682 Simplifying x = -0.203138682Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.536472022, -0.203138682}
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