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Simplifying 28x2 + -46x + -40 = 0 Reorder the terms: -40 + -46x + 28x2 = 0 Solving -40 + -46x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -23x + 14x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + -23x + 14x2)' equal to zero and attempt to solve: Simplifying -20 + -23x + 14x2 = 0 Solving -20 + -23x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.428571429 + -1.642857143x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -1.642857143x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -1.642857143x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -1.642857143x + x2 = 0 + 1.428571429 -1.642857143x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -1.642857143x + x2 = 1.428571429 The x term is -1.642857143x. Take half its coefficient (-0.8214285715). Square it (0.6747448981) and add it to both sides. Add '0.6747448981' to each side of the equation. -1.642857143x + 0.6747448981 + x2 = 1.428571429 + 0.6747448981 Reorder the terms: 0.6747448981 + -1.642857143x + x2 = 1.428571429 + 0.6747448981 Combine like terms: 1.428571429 + 0.6747448981 = 2.1033163271 0.6747448981 + -1.642857143x + x2 = 2.1033163271 Factor a perfect square on the left side: (x + -0.8214285715)(x + -0.8214285715) = 2.1033163271 Calculate the square root of the right side: 1.450281465 Break this problem into two subproblems by setting (x + -0.8214285715) equal to 1.450281465 and -1.450281465.Subproblem 1
x + -0.8214285715 = 1.450281465 Simplifying x + -0.8214285715 = 1.450281465 Reorder the terms: -0.8214285715 + x = 1.450281465 Solving -0.8214285715 + x = 1.450281465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8214285715' to each side of the equation. -0.8214285715 + 0.8214285715 + x = 1.450281465 + 0.8214285715 Combine like terms: -0.8214285715 + 0.8214285715 = 0.0000000000 0.0000000000 + x = 1.450281465 + 0.8214285715 x = 1.450281465 + 0.8214285715 Combine like terms: 1.450281465 + 0.8214285715 = 2.2717100365 x = 2.2717100365 Simplifying x = 2.2717100365Subproblem 2
x + -0.8214285715 = -1.450281465 Simplifying x + -0.8214285715 = -1.450281465 Reorder the terms: -0.8214285715 + x = -1.450281465 Solving -0.8214285715 + x = -1.450281465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8214285715' to each side of the equation. -0.8214285715 + 0.8214285715 + x = -1.450281465 + 0.8214285715 Combine like terms: -0.8214285715 + 0.8214285715 = 0.0000000000 0.0000000000 + x = -1.450281465 + 0.8214285715 x = -1.450281465 + 0.8214285715 Combine like terms: -1.450281465 + 0.8214285715 = -0.6288528935 x = -0.6288528935 Simplifying x = -0.6288528935Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2717100365, -0.6288528935}Solution
x = {2.2717100365, -0.6288528935}
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