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Simplifying 10x2 + 8x + -63 = 0 Reorder the terms: -63 + 8x + 10x2 = 0 Solving -63 + 8x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -6.3 + 0.8x + x2 = 0 Move the constant term to the right: Add '6.3' to each side of the equation. -6.3 + 0.8x + 6.3 + x2 = 0 + 6.3 Reorder the terms: -6.3 + 6.3 + 0.8x + x2 = 0 + 6.3 Combine like terms: -6.3 + 6.3 = 0.0 0.0 + 0.8x + x2 = 0 + 6.3 0.8x + x2 = 0 + 6.3 Combine like terms: 0 + 6.3 = 6.3 0.8x + x2 = 6.3 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 6.3 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 6.3 + 0.16 Combine like terms: 6.3 + 0.16 = 6.46 0.16 + 0.8x + x2 = 6.46 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 6.46 Calculate the square root of the right side: 2.541653005 Break this problem into two subproblems by setting (x + 0.4) equal to 2.541653005 and -2.541653005.Subproblem 1
x + 0.4 = 2.541653005 Simplifying x + 0.4 = 2.541653005 Reorder the terms: 0.4 + x = 2.541653005 Solving 0.4 + x = 2.541653005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.541653005 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.541653005 + -0.4 x = 2.541653005 + -0.4 Combine like terms: 2.541653005 + -0.4 = 2.141653005 x = 2.141653005 Simplifying x = 2.141653005Subproblem 2
x + 0.4 = -2.541653005 Simplifying x + 0.4 = -2.541653005 Reorder the terms: 0.4 + x = -2.541653005 Solving 0.4 + x = -2.541653005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.541653005 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.541653005 + -0.4 x = -2.541653005 + -0.4 Combine like terms: -2.541653005 + -0.4 = -2.941653005 x = -2.941653005 Simplifying x = -2.941653005Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.141653005, -2.941653005}
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