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Simplifying 7x2 = 72x + 3 Reorder the terms: 7x2 = 3 + 72x Solving 7x2 = 3 + 72x Solving for variable 'x'. Reorder the terms: -3 + -72x + 7x2 = 3 + 72x + -3 + -72x Reorder the terms: -3 + -72x + 7x2 = 3 + -3 + 72x + -72x Combine like terms: 3 + -3 = 0 -3 + -72x + 7x2 = 0 + 72x + -72x -3 + -72x + 7x2 = 72x + -72x Combine like terms: 72x + -72x = 0 -3 + -72x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -10.28571429x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -10.28571429x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -10.28571429x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -10.28571429x + x2 = 0 + 0.4285714286 -10.28571429x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -10.28571429x + x2 = 0.4285714286 The x term is -10.28571429x. Take half its coefficient (-5.142857145). Square it (26.44897961) and add it to both sides. Add '26.44897961' to each side of the equation. -10.28571429x + 26.44897961 + x2 = 0.4285714286 + 26.44897961 Reorder the terms: 26.44897961 + -10.28571429x + x2 = 0.4285714286 + 26.44897961 Combine like terms: 0.4285714286 + 26.44897961 = 26.8775510386 26.44897961 + -10.28571429x + x2 = 26.8775510386 Factor a perfect square on the left side: (x + -5.142857145)(x + -5.142857145) = 26.8775510386 Calculate the square root of the right side: 5.184356377 Break this problem into two subproblems by setting (x + -5.142857145) equal to 5.184356377 and -5.184356377.Subproblem 1
x + -5.142857145 = 5.184356377 Simplifying x + -5.142857145 = 5.184356377 Reorder the terms: -5.142857145 + x = 5.184356377 Solving -5.142857145 + x = 5.184356377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.142857145' to each side of the equation. -5.142857145 + 5.142857145 + x = 5.184356377 + 5.142857145 Combine like terms: -5.142857145 + 5.142857145 = 0.000000000 0.000000000 + x = 5.184356377 + 5.142857145 x = 5.184356377 + 5.142857145 Combine like terms: 5.184356377 + 5.142857145 = 10.327213522 x = 10.327213522 Simplifying x = 10.327213522Subproblem 2
x + -5.142857145 = -5.184356377 Simplifying x + -5.142857145 = -5.184356377 Reorder the terms: -5.142857145 + x = -5.184356377 Solving -5.142857145 + x = -5.184356377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.142857145' to each side of the equation. -5.142857145 + 5.142857145 + x = -5.184356377 + 5.142857145 Combine like terms: -5.142857145 + 5.142857145 = 0.000000000 0.000000000 + x = -5.184356377 + 5.142857145 x = -5.184356377 + 5.142857145 Combine like terms: -5.184356377 + 5.142857145 = -0.041499232 x = -0.041499232 Simplifying x = -0.041499232Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.327213522, -0.041499232}
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