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Simplifying -0.66x2 + 14x + 4 = 0 Reorder the terms: 4 + 14x + -0.66x2 = 0 Solving 4 + 14x + -0.66x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.66 the coefficient of the squared term: Divide each side by '-0.66'. -6.060606061 + -21.21212121x + x2 = 0 Move the constant term to the right: Add '6.060606061' to each side of the equation. -6.060606061 + -21.21212121x + 6.060606061 + x2 = 0 + 6.060606061 Reorder the terms: -6.060606061 + 6.060606061 + -21.21212121x + x2 = 0 + 6.060606061 Combine like terms: -6.060606061 + 6.060606061 = 0.000000000 0.000000000 + -21.21212121x + x2 = 0 + 6.060606061 -21.21212121x + x2 = 0 + 6.060606061 Combine like terms: 0 + 6.060606061 = 6.060606061 -21.21212121x + x2 = 6.060606061 The x term is -21.21212121x. Take half its coefficient (-10.60606061). Square it (112.4885217) and add it to both sides. Add '112.4885217' to each side of the equation. -21.21212121x + 112.4885217 + x2 = 6.060606061 + 112.4885217 Reorder the terms: 112.4885217 + -21.21212121x + x2 = 6.060606061 + 112.4885217 Combine like terms: 6.060606061 + 112.4885217 = 118.549127761 112.4885217 + -21.21212121x + x2 = 118.549127761 Factor a perfect square on the left side: (x + -10.60606061)(x + -10.60606061) = 118.549127761 Calculate the square root of the right side: 10.888026808 Break this problem into two subproblems by setting (x + -10.60606061) equal to 10.888026808 and -10.888026808.Subproblem 1
x + -10.60606061 = 10.888026808 Simplifying x + -10.60606061 = 10.888026808 Reorder the terms: -10.60606061 + x = 10.888026808 Solving -10.60606061 + x = 10.888026808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.60606061' to each side of the equation. -10.60606061 + 10.60606061 + x = 10.888026808 + 10.60606061 Combine like terms: -10.60606061 + 10.60606061 = 0.00000000 0.00000000 + x = 10.888026808 + 10.60606061 x = 10.888026808 + 10.60606061 Combine like terms: 10.888026808 + 10.60606061 = 21.494087418 x = 21.494087418 Simplifying x = 21.494087418Subproblem 2
x + -10.60606061 = -10.888026808 Simplifying x + -10.60606061 = -10.888026808 Reorder the terms: -10.60606061 + x = -10.888026808 Solving -10.60606061 + x = -10.888026808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.60606061' to each side of the equation. -10.60606061 + 10.60606061 + x = -10.888026808 + 10.60606061 Combine like terms: -10.60606061 + 10.60606061 = 0.00000000 0.00000000 + x = -10.888026808 + 10.60606061 x = -10.888026808 + 10.60606061 Combine like terms: -10.888026808 + 10.60606061 = -0.281966198 x = -0.281966198 Simplifying x = -0.281966198Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.494087418, -0.281966198}
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