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Simplifying 3x2 + 7x = 270 Reorder the terms: 7x + 3x2 = 270 Solving 7x + 3x2 = 270 Solving for variable 'x'. Reorder the terms: -270 + 7x + 3x2 = 270 + -270 Combine like terms: 270 + -270 = 0 -270 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -90 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 2.333333333x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 2.333333333x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 2.333333333x + x2 = 0 + 90 2.333333333x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 2.333333333x + x2 = 90 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 = 90 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 90 + 1.361111112 Combine like terms: 90 + 1.361111112 = 91.361111112 1.361111112 + 2.333333333x + x2 = 91.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 91.361111112 Calculate the square root of the right side: 9.558300639 Break this problem into two subproblems by setting (x + 1.166666667) equal to 9.558300639 and -9.558300639.Subproblem 1
x + 1.166666667 = 9.558300639 Simplifying x + 1.166666667 = 9.558300639 Reorder the terms: 1.166666667 + x = 9.558300639 Solving 1.166666667 + x = 9.558300639 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 = 9.558300639 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 9.558300639 + -1.166666667 x = 9.558300639 + -1.166666667 Combine like terms: 9.558300639 + -1.166666667 = 8.391633972 x = 8.391633972 Simplifying x = 8.391633972Subproblem 2
x + 1.166666667 = -9.558300639 Simplifying x + 1.166666667 = -9.558300639 Reorder the terms: 1.166666667 + x = -9.558300639 Solving 1.166666667 + x = -9.558300639 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 = -9.558300639 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -9.558300639 + -1.166666667 x = -9.558300639 + -1.166666667 Combine like terms: -9.558300639 + -1.166666667 = -10.724967306 x = -10.724967306 Simplifying x = -10.724967306Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.391633972, -10.724967306}
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