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Simplifying 6.02(0.12 + -0.70x + x2) = x (0.12 * 6.02 + -0.70x * 6.02 + x2 * 6.02) = x (0.7224 + -4.214x + 6.02x2) = x Solving 0.7224 + -4.214x + 6.02x2 = x Solving for variable 'x'. Reorder the terms: 0.7224 + -4.214x + -1x + 6.02x2 = x + -1x Combine like terms: -4.214x + -1x = -5.214x 0.7224 + -5.214x + 6.02x2 = x + -1x Combine like terms: x + -1x = 0 0.7224 + -5.214x + 6.02x2 = 0 Begin completing the square. Divide all terms by 6.02 the coefficient of the squared term: Divide each side by '6.02'. 0.12 + -0.8661129568x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.8661129568x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.8661129568x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.8661129568x + x2 = 0 + -0.12 -0.8661129568x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.8661129568x + x2 = -0.12 The x term is -0.8661129568x. Take half its coefficient (-0.4330564784). Square it (0.1875379135) and add it to both sides. Add '0.1875379135' to each side of the equation. -0.8661129568x + 0.1875379135 + x2 = -0.12 + 0.1875379135 Reorder the terms: 0.1875379135 + -0.8661129568x + x2 = -0.12 + 0.1875379135 Combine like terms: -0.12 + 0.1875379135 = 0.0675379135 0.1875379135 + -0.8661129568x + x2 = 0.0675379135 Factor a perfect square on the left side: (x + -0.4330564784)(x + -0.4330564784) = 0.0675379135 Calculate the square root of the right side: 0.259880575 Break this problem into two subproblems by setting (x + -0.4330564784) equal to 0.259880575 and -0.259880575.Subproblem 1
x + -0.4330564784 = 0.259880575 Simplifying x + -0.4330564784 = 0.259880575 Reorder the terms: -0.4330564784 + x = 0.259880575 Solving -0.4330564784 + x = 0.259880575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4330564784' to each side of the equation. -0.4330564784 + 0.4330564784 + x = 0.259880575 + 0.4330564784 Combine like terms: -0.4330564784 + 0.4330564784 = 0.0000000000 0.0000000000 + x = 0.259880575 + 0.4330564784 x = 0.259880575 + 0.4330564784 Combine like terms: 0.259880575 + 0.4330564784 = 0.6929370534 x = 0.6929370534 Simplifying x = 0.6929370534Subproblem 2
x + -0.4330564784 = -0.259880575 Simplifying x + -0.4330564784 = -0.259880575 Reorder the terms: -0.4330564784 + x = -0.259880575 Solving -0.4330564784 + x = -0.259880575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4330564784' to each side of the equation. -0.4330564784 + 0.4330564784 + x = -0.259880575 + 0.4330564784 Combine like terms: -0.4330564784 + 0.4330564784 = 0.0000000000 0.0000000000 + x = -0.259880575 + 0.4330564784 x = -0.259880575 + 0.4330564784 Combine like terms: -0.259880575 + 0.4330564784 = 0.1731759034 x = 0.1731759034 Simplifying x = 0.1731759034Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6929370534, 0.1731759034}
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