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Simplifying -3x2 + 9x + 30 = 1 Reorder the terms: 30 + 9x + -3x2 = 1 Solving 30 + 9x + -3x2 = 1 Solving for variable 'x'. Reorder the terms: 30 + -1 + 9x + -3x2 = 1 + -1 Combine like terms: 30 + -1 = 29 29 + 9x + -3x2 = 1 + -1 Combine like terms: 1 + -1 = 0 29 + 9x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -9.666666667 + -3x + x2 = 0 Move the constant term to the right: Add '9.666666667' to each side of the equation. -9.666666667 + -3x + 9.666666667 + x2 = 0 + 9.666666667 Reorder the terms: -9.666666667 + 9.666666667 + -3x + x2 = 0 + 9.666666667 Combine like terms: -9.666666667 + 9.666666667 = 0.000000000 0.000000000 + -3x + x2 = 0 + 9.666666667 -3x + x2 = 0 + 9.666666667 Combine like terms: 0 + 9.666666667 = 9.666666667 -3x + x2 = 9.666666667 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 9.666666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 9.666666667 + 2.25 Combine like terms: 9.666666667 + 2.25 = 11.916666667 2.25 + -3x + x2 = 11.916666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 11.916666667 Calculate the square root of the right side: 3.45205253 Break this problem into two subproblems by setting (x + -1.5) equal to 3.45205253 and -3.45205253.Subproblem 1
x + -1.5 = 3.45205253 Simplifying x + -1.5 = 3.45205253 Reorder the terms: -1.5 + x = 3.45205253 Solving -1.5 + x = 3.45205253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.45205253 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.45205253 + 1.5 x = 3.45205253 + 1.5 Combine like terms: 3.45205253 + 1.5 = 4.95205253 x = 4.95205253 Simplifying x = 4.95205253Subproblem 2
x + -1.5 = -3.45205253 Simplifying x + -1.5 = -3.45205253 Reorder the terms: -1.5 + x = -3.45205253 Solving -1.5 + x = -3.45205253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.45205253 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.45205253 + 1.5 x = -3.45205253 + 1.5 Combine like terms: -3.45205253 + 1.5 = -1.95205253 x = -1.95205253 Simplifying x = -1.95205253Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.95205253, -1.95205253}
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