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Simplifying 7x2 + -63 = x2 + -5x Reorder the terms: -63 + 7x2 = x2 + -5x Reorder the terms: -63 + 7x2 = -5x + x2 Solving -63 + 7x2 = -5x + x2 Solving for variable 'x'. Reorder the terms: -63 + 5x + 7x2 + -1x2 = -5x + x2 + 5x + -1x2 Combine like terms: 7x2 + -1x2 = 6x2 -63 + 5x + 6x2 = -5x + x2 + 5x + -1x2 Reorder the terms: -63 + 5x + 6x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 -63 + 5x + 6x2 = 0 + x2 + -1x2 -63 + 5x + 6x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -63 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.5 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 0.8333333333x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 0.8333333333x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 0.8333333333x + x2 = 0 + 10.5 0.8333333333x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 0.8333333333x + x2 = 10.5 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 10.5 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 10.5 + 0.1736111111 Combine like terms: 10.5 + 0.1736111111 = 10.6736111111 0.1736111111 + 0.8333333333x + x2 = 10.6736111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 10.6736111111 Calculate the square root of the right side: 3.267049297 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 3.267049297 and -3.267049297.Subproblem 1
x + 0.4166666667 = 3.267049297 Simplifying x + 0.4166666667 = 3.267049297 Reorder the terms: 0.4166666667 + x = 3.267049297 Solving 0.4166666667 + x = 3.267049297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 3.267049297 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 3.267049297 + -0.4166666667 x = 3.267049297 + -0.4166666667 Combine like terms: 3.267049297 + -0.4166666667 = 2.8503826303 x = 2.8503826303 Simplifying x = 2.8503826303Subproblem 2
x + 0.4166666667 = -3.267049297 Simplifying x + 0.4166666667 = -3.267049297 Reorder the terms: 0.4166666667 + x = -3.267049297 Solving 0.4166666667 + x = -3.267049297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -3.267049297 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -3.267049297 + -0.4166666667 x = -3.267049297 + -0.4166666667 Combine like terms: -3.267049297 + -0.4166666667 = -3.6837159637 x = -3.6837159637 Simplifying x = -3.6837159637Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8503826303, -3.6837159637}
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