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Simplifying -28x2 + 728x + 7812 = 9700 Reorder the terms: 7812 + 728x + -28x2 = 9700 Solving 7812 + 728x + -28x2 = 9700 Solving for variable 'x'. Reorder the terms: 7812 + -9700 + 728x + -28x2 = 9700 + -9700 Combine like terms: 7812 + -9700 = -1888 -1888 + 728x + -28x2 = 9700 + -9700 Combine like terms: 9700 + -9700 = 0 -1888 + 728x + -28x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-472 + 182x + -7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-472 + 182x + -7x2)' equal to zero and attempt to solve: Simplifying -472 + 182x + -7x2 = 0 Solving -472 + 182x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 67.42857143 + -26x + x2 = 0 Move the constant term to the right: Add '-67.42857143' to each side of the equation. 67.42857143 + -26x + -67.42857143 + x2 = 0 + -67.42857143 Reorder the terms: 67.42857143 + -67.42857143 + -26x + x2 = 0 + -67.42857143 Combine like terms: 67.42857143 + -67.42857143 = 0.00000000 0.00000000 + -26x + x2 = 0 + -67.42857143 -26x + x2 = 0 + -67.42857143 Combine like terms: 0 + -67.42857143 = -67.42857143 -26x + x2 = -67.42857143 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -67.42857143 + 169 Reorder the terms: 169 + -26x + x2 = -67.42857143 + 169 Combine like terms: -67.42857143 + 169 = 101.57142857 169 + -26x + x2 = 101.57142857 Factor a perfect square on the left side: (x + -13)(x + -13) = 101.57142857 Calculate the square root of the right side: 10.078265157 Break this problem into two subproblems by setting (x + -13) equal to 10.078265157 and -10.078265157.Subproblem 1
x + -13 = 10.078265157 Simplifying x + -13 = 10.078265157 Reorder the terms: -13 + x = 10.078265157 Solving -13 + x = 10.078265157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 10.078265157 + 13 Combine like terms: -13 + 13 = 0 0 + x = 10.078265157 + 13 x = 10.078265157 + 13 Combine like terms: 10.078265157 + 13 = 23.078265157 x = 23.078265157 Simplifying x = 23.078265157Subproblem 2
x + -13 = -10.078265157 Simplifying x + -13 = -10.078265157 Reorder the terms: -13 + x = -10.078265157 Solving -13 + x = -10.078265157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -10.078265157 + 13 Combine like terms: -13 + 13 = 0 0 + x = -10.078265157 + 13 x = -10.078265157 + 13 Combine like terms: -10.078265157 + 13 = 2.921734843 x = 2.921734843 Simplifying x = 2.921734843Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.078265157, 2.921734843}Solution
x = {23.078265157, 2.921734843}
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