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Simplifying 3x2 + 7x = 420 Reorder the terms: 7x + 3x2 = 420 Solving 7x + 3x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + 7x + 3x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -140 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 2.333333333x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 2.333333333x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 2.333333333x + x2 = 0 + 140 2.333333333x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 2.333333333x + x2 = 140 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 = 140 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 140 + 1.361111112 Combine like terms: 140 + 1.361111112 = 141.361111112 1.361111112 + 2.333333333x + x2 = 141.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 141.361111112 Calculate the square root of the right side: 11.889537885 Break this problem into two subproblems by setting (x + 1.166666667) equal to 11.889537885 and -11.889537885.Subproblem 1
x + 1.166666667 = 11.889537885 Simplifying x + 1.166666667 = 11.889537885 Reorder the terms: 1.166666667 + x = 11.889537885 Solving 1.166666667 + x = 11.889537885 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 = 11.889537885 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 11.889537885 + -1.166666667 x = 11.889537885 + -1.166666667 Combine like terms: 11.889537885 + -1.166666667 = 10.722871218 x = 10.722871218 Simplifying x = 10.722871218Subproblem 2
x + 1.166666667 = -11.889537885 Simplifying x + 1.166666667 = -11.889537885 Reorder the terms: 1.166666667 + x = -11.889537885 Solving 1.166666667 + x = -11.889537885 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 = -11.889537885 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -11.889537885 + -1.166666667 x = -11.889537885 + -1.166666667 Combine like terms: -11.889537885 + -1.166666667 = -13.056204552 x = -13.056204552 Simplifying x = -13.056204552Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.722871218, -13.056204552}
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