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Simplifying 7x2 = 10x + 45 Reorder the terms: 7x2 = 45 + 10x Solving 7x2 = 45 + 10x Solving for variable 'x'. Reorder the terms: -45 + -10x + 7x2 = 45 + 10x + -45 + -10x Reorder the terms: -45 + -10x + 7x2 = 45 + -45 + 10x + -10x Combine like terms: 45 + -45 = 0 -45 + -10x + 7x2 = 0 + 10x + -10x -45 + -10x + 7x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -45 + -10x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6.428571429 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '6.428571429' to each side of the equation. -6.428571429 + -1.428571429x + 6.428571429 + x2 = 0 + 6.428571429 Reorder the terms: -6.428571429 + 6.428571429 + -1.428571429x + x2 = 0 + 6.428571429 Combine like terms: -6.428571429 + 6.428571429 = 0.000000000 0.000000000 + -1.428571429x + x2 = 0 + 6.428571429 -1.428571429x + x2 = 0 + 6.428571429 Combine like terms: 0 + 6.428571429 = 6.428571429 -1.428571429x + x2 = 6.428571429 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 6.428571429 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 6.428571429 + 0.5102040819 Combine like terms: 6.428571429 + 0.5102040819 = 6.9387755109 0.5102040819 + -1.428571429x + x2 = 6.9387755109 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 6.9387755109 Calculate the square root of the right side: 2.634155559 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 2.634155559 and -2.634155559.Subproblem 1
x + -0.7142857145 = 2.634155559 Simplifying x + -0.7142857145 = 2.634155559 Reorder the terms: -0.7142857145 + x = 2.634155559 Solving -0.7142857145 + x = 2.634155559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 2.634155559 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 2.634155559 + 0.7142857145 x = 2.634155559 + 0.7142857145 Combine like terms: 2.634155559 + 0.7142857145 = 3.3484412735 x = 3.3484412735 Simplifying x = 3.3484412735Subproblem 2
x + -0.7142857145 = -2.634155559 Simplifying x + -0.7142857145 = -2.634155559 Reorder the terms: -0.7142857145 + x = -2.634155559 Solving -0.7142857145 + x = -2.634155559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -2.634155559 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -2.634155559 + 0.7142857145 x = -2.634155559 + 0.7142857145 Combine like terms: -2.634155559 + 0.7142857145 = -1.9198698445 x = -1.9198698445 Simplifying x = -1.9198698445Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3484412735, -1.9198698445}
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