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Simplifying -0.018x2 + 0.4x + -1.4 = 0 Reorder the terms: -1.4 + 0.4x + -0.018x2 = 0 Solving -1.4 + 0.4x + -0.018x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.018 the coefficient of the squared term: Divide each side by '-0.018'. 77.77777778 + -22.22222222x + x2 = 0 Move the constant term to the right: Add '-77.77777778' to each side of the equation. 77.77777778 + -22.22222222x + -77.77777778 + x2 = 0 + -77.77777778 Reorder the terms: 77.77777778 + -77.77777778 + -22.22222222x + x2 = 0 + -77.77777778 Combine like terms: 77.77777778 + -77.77777778 = 0.00000000 0.00000000 + -22.22222222x + x2 = 0 + -77.77777778 -22.22222222x + x2 = 0 + -77.77777778 Combine like terms: 0 + -77.77777778 = -77.77777778 -22.22222222x + x2 = -77.77777778 The x term is -22.22222222x. Take half its coefficient (-11.11111111). Square it (123.4567901) and add it to both sides. Add '123.4567901' to each side of the equation. -22.22222222x + 123.4567901 + x2 = -77.77777778 + 123.4567901 Reorder the terms: 123.4567901 + -22.22222222x + x2 = -77.77777778 + 123.4567901 Combine like terms: -77.77777778 + 123.4567901 = 45.67901232 123.4567901 + -22.22222222x + x2 = 45.67901232 Factor a perfect square on the left side: (x + -11.11111111)(x + -11.11111111) = 45.67901232 Calculate the square root of the right side: 6.758625032 Break this problem into two subproblems by setting (x + -11.11111111) equal to 6.758625032 and -6.758625032.Subproblem 1
x + -11.11111111 = 6.758625032 Simplifying x + -11.11111111 = 6.758625032 Reorder the terms: -11.11111111 + x = 6.758625032 Solving -11.11111111 + x = 6.758625032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.11111111' to each side of the equation. -11.11111111 + 11.11111111 + x = 6.758625032 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + x = 6.758625032 + 11.11111111 x = 6.758625032 + 11.11111111 Combine like terms: 6.758625032 + 11.11111111 = 17.869736142 x = 17.869736142 Simplifying x = 17.869736142Subproblem 2
x + -11.11111111 = -6.758625032 Simplifying x + -11.11111111 = -6.758625032 Reorder the terms: -11.11111111 + x = -6.758625032 Solving -11.11111111 + x = -6.758625032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.11111111' to each side of the equation. -11.11111111 + 11.11111111 + x = -6.758625032 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + x = -6.758625032 + 11.11111111 x = -6.758625032 + 11.11111111 Combine like terms: -6.758625032 + 11.11111111 = 4.352486078 x = 4.352486078 Simplifying x = 4.352486078Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.869736142, 4.352486078}
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