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Simplifying 10x2 + -70x + -63 = 0 Reorder the terms: -63 + -70x + 10x2 = 0 Solving -63 + -70x + 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 + -7x + x2 = 0 Move the constant term to the right: Add '6.3' to each side of the equation. -6.3 + -7x + 6.3 + x2 = 0 + 6.3 Reorder the terms: -6.3 + 6.3 + -7x + x2 = 0 + 6.3 Combine like terms: -6.3 + 6.3 = 0.0 0.0 + -7x + x2 = 0 + 6.3 -7x + x2 = 0 + 6.3 Combine like terms: 0 + 6.3 = 6.3 -7x + x2 = 6.3 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 = 6.3 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 6.3 + 12.25 Combine like terms: 6.3 + 12.25 = 18.55 12.25 + -7x + x2 = 18.55 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 18.55 Calculate the square root of the right side: 4.306971093 Break this problem into two subproblems by setting (x + -3.5) equal to 4.306971093 and -4.306971093.Subproblem 1
x + -3.5 = 4.306971093 Simplifying x + -3.5 = 4.306971093 Reorder the terms: -3.5 + x = 4.306971093 Solving -3.5 + x = 4.306971093 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 = 4.306971093 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.306971093 + 3.5 x = 4.306971093 + 3.5 Combine like terms: 4.306971093 + 3.5 = 7.806971093 x = 7.806971093 Simplifying x = 7.806971093Subproblem 2
x + -3.5 = -4.306971093 Simplifying x + -3.5 = -4.306971093 Reorder the terms: -3.5 + x = -4.306971093 Solving -3.5 + x = -4.306971093 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 = -4.306971093 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.306971093 + 3.5 x = -4.306971093 + 3.5 Combine like terms: -4.306971093 + 3.5 = -0.806971093 x = -0.806971093 Simplifying x = -0.806971093Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.806971093, -0.806971093}
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