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Simplifying 3x2 + 6x + -30 = 65 Reorder the terms: -30 + 6x + 3x2 = 65 Solving -30 + 6x + 3x2 = 65 Solving for variable 'x'. Reorder the terms: -30 + -65 + 6x + 3x2 = 65 + -65 Combine like terms: -30 + -65 = -95 -95 + 6x + 3x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -95 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -31.66666667 + 2x + x2 = 0 Move the constant term to the right: Add '31.66666667' to each side of the equation. -31.66666667 + 2x + 31.66666667 + x2 = 0 + 31.66666667 Reorder the terms: -31.66666667 + 31.66666667 + 2x + x2 = 0 + 31.66666667 Combine like terms: -31.66666667 + 31.66666667 = 0.00000000 0.00000000 + 2x + x2 = 0 + 31.66666667 2x + x2 = 0 + 31.66666667 Combine like terms: 0 + 31.66666667 = 31.66666667 2x + x2 = 31.66666667 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 31.66666667 + 1 Reorder the terms: 1 + 2x + x2 = 31.66666667 + 1 Combine like terms: 31.66666667 + 1 = 32.66666667 1 + 2x + x2 = 32.66666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 32.66666667 Calculate the square root of the right side: 5.715476067 Break this problem into two subproblems by setting (x + 1) equal to 5.715476067 and -5.715476067.Subproblem 1
x + 1 = 5.715476067 Simplifying x + 1 = 5.715476067 Reorder the terms: 1 + x = 5.715476067 Solving 1 + x = 5.715476067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.715476067 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.715476067 + -1 x = 5.715476067 + -1 Combine like terms: 5.715476067 + -1 = 4.715476067 x = 4.715476067 Simplifying x = 4.715476067Subproblem 2
x + 1 = -5.715476067 Simplifying x + 1 = -5.715476067 Reorder the terms: 1 + x = -5.715476067 Solving 1 + x = -5.715476067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.715476067 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.715476067 + -1 x = -5.715476067 + -1 Combine like terms: -5.715476067 + -1 = -6.715476067 x = -6.715476067 Simplifying x = -6.715476067Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.715476067, -6.715476067}
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