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Simplifying 3x2 + 7x + -5 = 88 Reorder the terms: -5 + 7x + 3x2 = 88 Solving -5 + 7x + 3x2 = 88 Solving for variable 'x'. Reorder the terms: -5 + -88 + 7x + 3x2 = 88 + -88 Combine like terms: -5 + -88 = -93 -93 + 7x + 3x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -93 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -31 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 2.333333333x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 2.333333333x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 2.333333333x + x2 = 0 + 31 2.333333333x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 2.333333333x + x2 = 31 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 = 31 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 31 + 1.361111112 Combine like terms: 31 + 1.361111112 = 32.361111112 1.361111112 + 2.333333333x + x2 = 32.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 32.361111112 Calculate the square root of the right side: 5.688682722 Break this problem into two subproblems by setting (x + 1.166666667) equal to 5.688682722 and -5.688682722.Subproblem 1
x + 1.166666667 = 5.688682722 Simplifying x + 1.166666667 = 5.688682722 Reorder the terms: 1.166666667 + x = 5.688682722 Solving 1.166666667 + x = 5.688682722 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 = 5.688682722 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 5.688682722 + -1.166666667 x = 5.688682722 + -1.166666667 Combine like terms: 5.688682722 + -1.166666667 = 4.522016055 x = 4.522016055 Simplifying x = 4.522016055Subproblem 2
x + 1.166666667 = -5.688682722 Simplifying x + 1.166666667 = -5.688682722 Reorder the terms: 1.166666667 + x = -5.688682722 Solving 1.166666667 + x = -5.688682722 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 = -5.688682722 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -5.688682722 + -1.166666667 x = -5.688682722 + -1.166666667 Combine like terms: -5.688682722 + -1.166666667 = -6.855349389 x = -6.855349389 Simplifying x = -6.855349389Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.522016055, -6.855349389}
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