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Simplifying 14x2 + -12x + -2 = 145 Reorder the terms: -2 + -12x + 14x2 = 145 Solving -2 + -12x + 14x2 = 145 Solving for variable 'x'. Reorder the terms: -2 + -145 + -12x + 14x2 = 145 + -145 Combine like terms: -2 + -145 = -147 -147 + -12x + 14x2 = 145 + -145 Combine like terms: 145 + -145 = 0 -147 + -12x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -10.5 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -0.8571428571x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -0.8571428571x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -0.8571428571x + x2 = 0 + 10.5 -0.8571428571x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -0.8571428571x + x2 = 10.5 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 10.5 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 10.5 + 0.1836734694 Combine like terms: 10.5 + 0.1836734694 = 10.6836734694 0.1836734694 + -0.8571428571x + x2 = 10.6836734694 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 10.6836734694 Calculate the square root of the right side: 3.268588911 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 3.268588911 and -3.268588911.Subproblem 1
x + -0.4285714286 = 3.268588911 Simplifying x + -0.4285714286 = 3.268588911 Reorder the terms: -0.4285714286 + x = 3.268588911 Solving -0.4285714286 + x = 3.268588911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 3.268588911 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 3.268588911 + 0.4285714286 x = 3.268588911 + 0.4285714286 Combine like terms: 3.268588911 + 0.4285714286 = 3.6971603396 x = 3.6971603396 Simplifying x = 3.6971603396Subproblem 2
x + -0.4285714286 = -3.268588911 Simplifying x + -0.4285714286 = -3.268588911 Reorder the terms: -0.4285714286 + x = -3.268588911 Solving -0.4285714286 + x = -3.268588911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -3.268588911 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -3.268588911 + 0.4285714286 x = -3.268588911 + 0.4285714286 Combine like terms: -3.268588911 + 0.4285714286 = -2.8400174824 x = -2.8400174824 Simplifying x = -2.8400174824Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6971603396, -2.8400174824}
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