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Simplifying 3x2 + 7x = 210 Reorder the terms: 7x + 3x2 = 210 Solving 7x + 3x2 = 210 Solving for variable 'x'. Reorder the terms: -210 + 7x + 3x2 = 210 + -210 Combine like terms: 210 + -210 = 0 -210 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -70 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 2.333333333x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 2.333333333x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 2.333333333x + x2 = 0 + 70 2.333333333x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 2.333333333x + x2 = 70 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 = 70 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 70 + 1.361111112 Combine like terms: 70 + 1.361111112 = 71.361111112 1.361111112 + 2.333333333x + x2 = 71.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 71.361111112 Calculate the square root of the right side: 8.447550598 Break this problem into two subproblems by setting (x + 1.166666667) equal to 8.447550598 and -8.447550598.Subproblem 1
x + 1.166666667 = 8.447550598 Simplifying x + 1.166666667 = 8.447550598 Reorder the terms: 1.166666667 + x = 8.447550598 Solving 1.166666667 + x = 8.447550598 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 = 8.447550598 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 8.447550598 + -1.166666667 x = 8.447550598 + -1.166666667 Combine like terms: 8.447550598 + -1.166666667 = 7.280883931 x = 7.280883931 Simplifying x = 7.280883931Subproblem 2
x + 1.166666667 = -8.447550598 Simplifying x + 1.166666667 = -8.447550598 Reorder the terms: 1.166666667 + x = -8.447550598 Solving 1.166666667 + x = -8.447550598 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 = -8.447550598 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -8.447550598 + -1.166666667 x = -8.447550598 + -1.166666667 Combine like terms: -8.447550598 + -1.166666667 = -9.614217265 x = -9.614217265 Simplifying x = -9.614217265Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.280883931, -9.614217265}
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