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Simplifying 18x + 8 = 3x2 + -0.75 Reorder the terms: 8 + 18x = 3x2 + -0.75 Reorder the terms: 8 + 18x = -0.75 + 3x2 Solving 8 + 18x = -0.75 + 3x2 Solving for variable 'x'. Reorder the terms: 8 + 0.75 + 18x + -3x2 = -0.75 + 3x2 + 0.75 + -3x2 Combine like terms: 8 + 0.75 = 8.75 8.75 + 18x + -3x2 = -0.75 + 3x2 + 0.75 + -3x2 Reorder the terms: 8.75 + 18x + -3x2 = -0.75 + 0.75 + 3x2 + -3x2 Combine like terms: -0.75 + 0.75 = 0.00 8.75 + 18x + -3x2 = 0.00 + 3x2 + -3x2 8.75 + 18x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 8.75 + 18x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.916666667 + -6x + x2 = 0 Move the constant term to the right: Add '2.916666667' to each side of the equation. -2.916666667 + -6x + 2.916666667 + x2 = 0 + 2.916666667 Reorder the terms: -2.916666667 + 2.916666667 + -6x + x2 = 0 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + -6x + x2 = 0 + 2.916666667 -6x + x2 = 0 + 2.916666667 Combine like terms: 0 + 2.916666667 = 2.916666667 -6x + x2 = 2.916666667 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 2.916666667 + 9 Reorder the terms: 9 + -6x + x2 = 2.916666667 + 9 Combine like terms: 2.916666667 + 9 = 11.916666667 9 + -6x + x2 = 11.916666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 11.916666667 Calculate the square root of the right side: 3.45205253 Break this problem into two subproblems by setting (x + -3) equal to 3.45205253 and -3.45205253.Subproblem 1
x + -3 = 3.45205253 Simplifying x + -3 = 3.45205253 Reorder the terms: -3 + x = 3.45205253 Solving -3 + x = 3.45205253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.45205253 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.45205253 + 3 x = 3.45205253 + 3 Combine like terms: 3.45205253 + 3 = 6.45205253 x = 6.45205253 Simplifying x = 6.45205253Subproblem 2
x + -3 = -3.45205253 Simplifying x + -3 = -3.45205253 Reorder the terms: -3 + x = -3.45205253 Solving -3 + x = -3.45205253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.45205253 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.45205253 + 3 x = -3.45205253 + 3 Combine like terms: -3.45205253 + 3 = -0.45205253 x = -0.45205253 Simplifying x = -0.45205253Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.45205253, -0.45205253}
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