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Simplifying 5x2 = 8x + 7 Reorder the terms: 5x2 = 7 + 8x Solving 5x2 = 7 + 8x Solving for variable 'x'. Reorder the terms: -7 + -8x + 5x2 = 7 + 8x + -7 + -8x Reorder the terms: -7 + -8x + 5x2 = 7 + -7 + 8x + -8x Combine like terms: 7 + -7 = 0 -7 + -8x + 5x2 = 0 + 8x + -8x -7 + -8x + 5x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -7 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -1.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1.6x + x2 = 0 + 1.4 -1.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1.6x + x2 = 1.4 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 1.4 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 1.4 + 0.64 Combine like terms: 1.4 + 0.64 = 2.04 0.64 + -1.6x + x2 = 2.04 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (x + -0.8) equal to 1.428285686 and -1.428285686.Subproblem 1
x + -0.8 = 1.428285686 Simplifying x + -0.8 = 1.428285686 Reorder the terms: -0.8 + x = 1.428285686 Solving -0.8 + x = 1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.428285686 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.428285686 + 0.8 x = 1.428285686 + 0.8 Combine like terms: 1.428285686 + 0.8 = 2.228285686 x = 2.228285686 Simplifying x = 2.228285686Subproblem 2
x + -0.8 = -1.428285686 Simplifying x + -0.8 = -1.428285686 Reorder the terms: -0.8 + x = -1.428285686 Solving -0.8 + x = -1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.428285686 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.428285686 + 0.8 x = -1.428285686 + 0.8 Combine like terms: -1.428285686 + 0.8 = -0.628285686 x = -0.628285686 Simplifying x = -0.628285686Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.228285686, -0.628285686}
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