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Simplifying 9x + -14x(x + -3) = 6 Reorder the terms: 9x + -14x(-3 + x) = 6 9x + (-3 * -14x + x * -14x) = 6 9x + (42x + -14x2) = 6 Combine like terms: 9x + 42x = 51x 51x + -14x2 = 6 Solving 51x + -14x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 51x + -14x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 51x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. 0.4285714286 + -3.642857143x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -3.642857143x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -3.642857143x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -3.642857143x + x2 = 0 + -0.4285714286 -3.642857143x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -3.642857143x + x2 = -0.4285714286 The x term is -3.642857143x. Take half its coefficient (-1.821428572). Square it (3.317602043) and add it to both sides. Add '3.317602043' to each side of the equation. -3.642857143x + 3.317602043 + x2 = -0.4285714286 + 3.317602043 Reorder the terms: 3.317602043 + -3.642857143x + x2 = -0.4285714286 + 3.317602043 Combine like terms: -0.4285714286 + 3.317602043 = 2.8890306144 3.317602043 + -3.642857143x + x2 = 2.8890306144 Factor a perfect square on the left side: (x + -1.821428572)(x + -1.821428572) = 2.8890306144 Calculate the square root of the right side: 1.699714863 Break this problem into two subproblems by setting (x + -1.821428572) equal to 1.699714863 and -1.699714863.Subproblem 1
x + -1.821428572 = 1.699714863 Simplifying x + -1.821428572 = 1.699714863 Reorder the terms: -1.821428572 + x = 1.699714863 Solving -1.821428572 + x = 1.699714863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.821428572' to each side of the equation. -1.821428572 + 1.821428572 + x = 1.699714863 + 1.821428572 Combine like terms: -1.821428572 + 1.821428572 = 0.000000000 0.000000000 + x = 1.699714863 + 1.821428572 x = 1.699714863 + 1.821428572 Combine like terms: 1.699714863 + 1.821428572 = 3.521143435 x = 3.521143435 Simplifying x = 3.521143435Subproblem 2
x + -1.821428572 = -1.699714863 Simplifying x + -1.821428572 = -1.699714863 Reorder the terms: -1.821428572 + x = -1.699714863 Solving -1.821428572 + x = -1.699714863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.821428572' to each side of the equation. -1.821428572 + 1.821428572 + x = -1.699714863 + 1.821428572 Combine like terms: -1.821428572 + 1.821428572 = 0.000000000 0.000000000 + x = -1.699714863 + 1.821428572 x = -1.699714863 + 1.821428572 Combine like terms: -1.699714863 + 1.821428572 = 0.121713709 x = 0.121713709 Simplifying x = 0.121713709Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.521143435, 0.121713709}
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