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Simplifying 3x2 + 6x = 146 Reorder the terms: 6x + 3x2 = 146 Solving 6x + 3x2 = 146 Solving for variable 'x'. Reorder the terms: -146 + 6x + 3x2 = 146 + -146 Combine like terms: 146 + -146 = 0 -146 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -48.66666667 + 2x + x2 = 0 Move the constant term to the right: Add '48.66666667' to each side of the equation. -48.66666667 + 2x + 48.66666667 + x2 = 0 + 48.66666667 Reorder the terms: -48.66666667 + 48.66666667 + 2x + x2 = 0 + 48.66666667 Combine like terms: -48.66666667 + 48.66666667 = 0.00000000 0.00000000 + 2x + x2 = 0 + 48.66666667 2x + x2 = 0 + 48.66666667 Combine like terms: 0 + 48.66666667 = 48.66666667 2x + x2 = 48.66666667 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 = 48.66666667 + 1 Reorder the terms: 1 + 2x + x2 = 48.66666667 + 1 Combine like terms: 48.66666667 + 1 = 49.66666667 1 + 2x + x2 = 49.66666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 49.66666667 Calculate the square root of the right side: 7.047458171 Break this problem into two subproblems by setting (x + 1) equal to 7.047458171 and -7.047458171.Subproblem 1
x + 1 = 7.047458171 Simplifying x + 1 = 7.047458171 Reorder the terms: 1 + x = 7.047458171 Solving 1 + x = 7.047458171 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 = 7.047458171 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.047458171 + -1 x = 7.047458171 + -1 Combine like terms: 7.047458171 + -1 = 6.047458171 x = 6.047458171 Simplifying x = 6.047458171Subproblem 2
x + 1 = -7.047458171 Simplifying x + 1 = -7.047458171 Reorder the terms: 1 + x = -7.047458171 Solving 1 + x = -7.047458171 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 = -7.047458171 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.047458171 + -1 x = -7.047458171 + -1 Combine like terms: -7.047458171 + -1 = -8.047458171 x = -8.047458171 Simplifying x = -8.047458171Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.047458171, -8.047458171}
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