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Simplifying 3x2 + -7x = 153 Reorder the terms: -7x + 3x2 = 153 Solving -7x + 3x2 = 153 Solving for variable 'x'. Reorder the terms: -153 + -7x + 3x2 = 153 + -153 Combine like terms: 153 + -153 = 0 -153 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -51 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '51' to each side of the equation. -51 + -2.333333333x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -2.333333333x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -2.333333333x + x2 = 0 + 51 -2.333333333x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -2.333333333x + x2 = 51 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 51 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 51 + 1.361111112 Combine like terms: 51 + 1.361111112 = 52.361111112 1.361111112 + -2.333333333x + x2 = 52.361111112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 52.361111112 Calculate the square root of the right side: 7.236097782 Break this problem into two subproblems by setting (x + -1.166666667) equal to 7.236097782 and -7.236097782.Subproblem 1
x + -1.166666667 = 7.236097782 Simplifying x + -1.166666667 = 7.236097782 Reorder the terms: -1.166666667 + x = 7.236097782 Solving -1.166666667 + x = 7.236097782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 7.236097782 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 7.236097782 + 1.166666667 x = 7.236097782 + 1.166666667 Combine like terms: 7.236097782 + 1.166666667 = 8.402764449 x = 8.402764449 Simplifying x = 8.402764449Subproblem 2
x + -1.166666667 = -7.236097782 Simplifying x + -1.166666667 = -7.236097782 Reorder the terms: -1.166666667 + x = -7.236097782 Solving -1.166666667 + x = -7.236097782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -7.236097782 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -7.236097782 + 1.166666667 x = -7.236097782 + 1.166666667 Combine like terms: -7.236097782 + 1.166666667 = -6.069431115 x = -6.069431115 Simplifying x = -6.069431115Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.402764449, -6.069431115}
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