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Simplifying 7x2 + -15 = 3x + 25 Reorder the terms: -15 + 7x2 = 3x + 25 Reorder the terms: -15 + 7x2 = 25 + 3x Solving -15 + 7x2 = 25 + 3x Solving for variable 'x'. Reorder the terms: -15 + -25 + -3x + 7x2 = 25 + 3x + -25 + -3x Combine like terms: -15 + -25 = -40 -40 + -3x + 7x2 = 25 + 3x + -25 + -3x Reorder the terms: -40 + -3x + 7x2 = 25 + -25 + 3x + -3x Combine like terms: 25 + -25 = 0 -40 + -3x + 7x2 = 0 + 3x + -3x -40 + -3x + 7x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -40 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.714285714 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + -0.4285714286x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + -0.4285714286x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + 5.714285714 -0.4285714286x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 -0.4285714286x + x2 = 5.714285714 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 5.714285714 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 5.714285714 + 0.04591836735 Combine like terms: 5.714285714 + 0.04591836735 = 5.76020408135 0.04591836735 + -0.4285714286x + x2 = 5.76020408135 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 5.76020408135 Calculate the square root of the right side: 2.400042517 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 2.400042517 and -2.400042517.Subproblem 1
x + -0.2142857143 = 2.400042517 Simplifying x + -0.2142857143 = 2.400042517 Reorder the terms: -0.2142857143 + x = 2.400042517 Solving -0.2142857143 + x = 2.400042517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 2.400042517 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 2.400042517 + 0.2142857143 x = 2.400042517 + 0.2142857143 Combine like terms: 2.400042517 + 0.2142857143 = 2.6143282313 x = 2.6143282313 Simplifying x = 2.6143282313Subproblem 2
x + -0.2142857143 = -2.400042517 Simplifying x + -0.2142857143 = -2.400042517 Reorder the terms: -0.2142857143 + x = -2.400042517 Solving -0.2142857143 + x = -2.400042517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -2.400042517 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -2.400042517 + 0.2142857143 x = -2.400042517 + 0.2142857143 Combine like terms: -2.400042517 + 0.2142857143 = -2.1857568027 x = -2.1857568027 Simplifying x = -2.1857568027Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6143282313, -2.1857568027}
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