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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 = 10.724967306 x = 10.724967306 Simplifying x = 10.724967306Subproblem 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 = -8.391633972 x = -8.391633972 Simplifying x = -8.391633972Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.724967306, -8.391633972}
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