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Simplifying 5x2 + 20x + -70 = -7 Reorder the terms: -70 + 20x + 5x2 = -7 Solving -70 + 20x + 5x2 = -7 Solving for variable 'x'. Reorder the terms: -70 + 7 + 20x + 5x2 = -7 + 7 Combine like terms: -70 + 7 = -63 -63 + 20x + 5x2 = -7 + 7 Combine like terms: -7 + 7 = 0 -63 + 20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.6 + 4x + x2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + 4x + 12.6 + x2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + 4x + x2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + 4x + x2 = 0 + 12.6 4x + x2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 4x + x2 = 12.6 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 12.6 + 4 Reorder the terms: 4 + 4x + x2 = 12.6 + 4 Combine like terms: 12.6 + 4 = 16.6 4 + 4x + x2 = 16.6 Factor a perfect square on the left side: (x + 2)(x + 2) = 16.6 Calculate the square root of the right side: 4.074309757 Break this problem into two subproblems by setting (x + 2) equal to 4.074309757 and -4.074309757.Subproblem 1
x + 2 = 4.074309757 Simplifying x + 2 = 4.074309757 Reorder the terms: 2 + x = 4.074309757 Solving 2 + x = 4.074309757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.074309757 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.074309757 + -2 x = 4.074309757 + -2 Combine like terms: 4.074309757 + -2 = 2.074309757 x = 2.074309757 Simplifying x = 2.074309757Subproblem 2
x + 2 = -4.074309757 Simplifying x + 2 = -4.074309757 Reorder the terms: 2 + x = -4.074309757 Solving 2 + x = -4.074309757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.074309757 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.074309757 + -2 x = -4.074309757 + -2 Combine like terms: -4.074309757 + -2 = -6.074309757 x = -6.074309757 Simplifying x = -6.074309757Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.074309757, -6.074309757}
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