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Simplifying 18x2 + 16x + -7 = 0 Reorder the terms: -7 + 16x + 18x2 = 0 Solving -7 + 16x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.3888888889 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.8888888889x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + 0.8888888889x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + 0.8888888889x + x2 = 0 + 0.3888888889 0.8888888889x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 0.8888888889x + x2 = 0.3888888889 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = 0.3888888889 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 0.3888888889 + 0.1975308642 Combine like terms: 0.3888888889 + 0.1975308642 = 0.5864197531 0.1975308642 + 0.8888888889x + x2 = 0.5864197531 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 0.5864197531 Calculate the square root of the right side: 0.765780486 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 0.765780486 and -0.765780486.Subproblem 1
x + 0.4444444445 = 0.765780486 Simplifying x + 0.4444444445 = 0.765780486 Reorder the terms: 0.4444444445 + x = 0.765780486 Solving 0.4444444445 + x = 0.765780486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 0.765780486 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 0.765780486 + -0.4444444445 x = 0.765780486 + -0.4444444445 Combine like terms: 0.765780486 + -0.4444444445 = 0.3213360415 x = 0.3213360415 Simplifying x = 0.3213360415Subproblem 2
x + 0.4444444445 = -0.765780486 Simplifying x + 0.4444444445 = -0.765780486 Reorder the terms: 0.4444444445 + x = -0.765780486 Solving 0.4444444445 + x = -0.765780486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -0.765780486 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -0.765780486 + -0.4444444445 x = -0.765780486 + -0.4444444445 Combine like terms: -0.765780486 + -0.4444444445 = -1.2102249305 x = -1.2102249305 Simplifying x = -1.2102249305Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3213360415, -1.2102249305}
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