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Simplifying 63x + 147 = 9x2 + 49 Reorder the terms: 147 + 63x = 9x2 + 49 Reorder the terms: 147 + 63x = 49 + 9x2 Solving 147 + 63x = 49 + 9x2 Solving for variable 'x'. Reorder the terms: 147 + -49 + 63x + -9x2 = 49 + 9x2 + -49 + -9x2 Combine like terms: 147 + -49 = 98 98 + 63x + -9x2 = 49 + 9x2 + -49 + -9x2 Reorder the terms: 98 + 63x + -9x2 = 49 + -49 + 9x2 + -9x2 Combine like terms: 49 + -49 = 0 98 + 63x + -9x2 = 0 + 9x2 + -9x2 98 + 63x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 98 + 63x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -10.88888889 + -7x + x2 = 0 Move the constant term to the right: Add '10.88888889' to each side of the equation. -10.88888889 + -7x + 10.88888889 + x2 = 0 + 10.88888889 Reorder the terms: -10.88888889 + 10.88888889 + -7x + x2 = 0 + 10.88888889 Combine like terms: -10.88888889 + 10.88888889 = 0.00000000 0.00000000 + -7x + x2 = 0 + 10.88888889 -7x + x2 = 0 + 10.88888889 Combine like terms: 0 + 10.88888889 = 10.88888889 -7x + x2 = 10.88888889 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 10.88888889 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 10.88888889 + 12.25 Combine like terms: 10.88888889 + 12.25 = 23.13888889 12.25 + -7x + x2 = 23.13888889 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 23.13888889 Calculate the square root of the right side: 4.810289897 Break this problem into two subproblems by setting (x + -3.5) equal to 4.810289897 and -4.810289897.Subproblem 1
x + -3.5 = 4.810289897 Simplifying x + -3.5 = 4.810289897 Reorder the terms: -3.5 + x = 4.810289897 Solving -3.5 + x = 4.810289897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.810289897 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.810289897 + 3.5 x = 4.810289897 + 3.5 Combine like terms: 4.810289897 + 3.5 = 8.310289897 x = 8.310289897 Simplifying x = 8.310289897Subproblem 2
x + -3.5 = -4.810289897 Simplifying x + -3.5 = -4.810289897 Reorder the terms: -3.5 + x = -4.810289897 Solving -3.5 + x = -4.810289897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.810289897 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.810289897 + 3.5 x = -4.810289897 + 3.5 Combine like terms: -4.810289897 + 3.5 = -1.310289897 x = -1.310289897 Simplifying x = -1.310289897Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.310289897, -1.310289897}
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