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Simplifying 164 = 0.93(x2) + 2.2x + 130 Reorder the terms: 164 = 130 + 2.2x + 0.93x2 Solving 164 = 130 + 2.2x + 0.93x2 Solving for variable 'x'. Combine like terms: 164 + -130 = 34 34 + -2.2x + -0.93x2 = 130 + 2.2x + 0.93x2 + -130 + -2.2x + -0.93x2 Reorder the terms: 34 + -2.2x + -0.93x2 = 130 + -130 + 2.2x + -2.2x + 0.93x2 + -0.93x2 Combine like terms: 130 + -130 = 0 34 + -2.2x + -0.93x2 = 0 + 2.2x + -2.2x + 0.93x2 + -0.93x2 34 + -2.2x + -0.93x2 = 2.2x + -2.2x + 0.93x2 + -0.93x2 Combine like terms: 2.2x + -2.2x = 0.0 34 + -2.2x + -0.93x2 = 0.0 + 0.93x2 + -0.93x2 34 + -2.2x + -0.93x2 = 0.93x2 + -0.93x2 Combine like terms: 0.93x2 + -0.93x2 = 0.00 34 + -2.2x + -0.93x2 = 0.00 Begin completing the square. Divide all terms by -0.93 the coefficient of the squared term: Divide each side by '-0.93'. -36.55913978 + 2.365591398x + x2 = 0 Move the constant term to the right: Add '36.55913978' to each side of the equation. -36.55913978 + 2.365591398x + 36.55913978 + x2 = 0 + 36.55913978 Reorder the terms: -36.55913978 + 36.55913978 + 2.365591398x + x2 = 0 + 36.55913978 Combine like terms: -36.55913978 + 36.55913978 = 0.00000000 0.00000000 + 2.365591398x + x2 = 0 + 36.55913978 2.365591398x + x2 = 0 + 36.55913978 Combine like terms: 0 + 36.55913978 = 36.55913978 2.365591398x + x2 = 36.55913978 The x term is 2.365591398x. Take half its coefficient (1.182795699). Square it (1.399005666) and add it to both sides. Add '1.399005666' to each side of the equation. 2.365591398x + 1.399005666 + x2 = 36.55913978 + 1.399005666 Reorder the terms: 1.399005666 + 2.365591398x + x2 = 36.55913978 + 1.399005666 Combine like terms: 36.55913978 + 1.399005666 = 37.958145446 1.399005666 + 2.365591398x + x2 = 37.958145446 Factor a perfect square on the left side: (x + 1.182795699)(x + 1.182795699) = 37.958145446 Calculate the square root of the right side: 6.161018215 Break this problem into two subproblems by setting (x + 1.182795699) equal to 6.161018215 and -6.161018215.Subproblem 1
x + 1.182795699 = 6.161018215 Simplifying x + 1.182795699 = 6.161018215 Reorder the terms: 1.182795699 + x = 6.161018215 Solving 1.182795699 + x = 6.161018215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.182795699' to each side of the equation. 1.182795699 + -1.182795699 + x = 6.161018215 + -1.182795699 Combine like terms: 1.182795699 + -1.182795699 = 0.000000000 0.000000000 + x = 6.161018215 + -1.182795699 x = 6.161018215 + -1.182795699 Combine like terms: 6.161018215 + -1.182795699 = 4.978222516 x = 4.978222516 Simplifying x = 4.978222516Subproblem 2
x + 1.182795699 = -6.161018215 Simplifying x + 1.182795699 = -6.161018215 Reorder the terms: 1.182795699 + x = -6.161018215 Solving 1.182795699 + x = -6.161018215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.182795699' to each side of the equation. 1.182795699 + -1.182795699 + x = -6.161018215 + -1.182795699 Combine like terms: 1.182795699 + -1.182795699 = 0.000000000 0.000000000 + x = -6.161018215 + -1.182795699 x = -6.161018215 + -1.182795699 Combine like terms: -6.161018215 + -1.182795699 = -7.343813914 x = -7.343813914 Simplifying x = -7.343813914Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.978222516, -7.343813914}
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