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Simplifying 0 = 5x2 + 4x + -7 Reorder the terms: 0 = -7 + 4x + 5x2 Solving 0 = -7 + 4x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + -4x + -5x2 = -7 + 4x + 5x2 + 7 + -4x + -5x2 Reorder the terms: 7 + -4x + -5x2 = -7 + 7 + 4x + -4x + 5x2 + -5x2 Combine like terms: -7 + 7 = 0 7 + -4x + -5x2 = 0 + 4x + -4x + 5x2 + -5x2 7 + -4x + -5x2 = 4x + -4x + 5x2 + -5x2 Combine like terms: 4x + -4x = 0 7 + -4x + -5x2 = 0 + 5x2 + -5x2 7 + -4x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 7 + -4x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.4 + 0.8x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 0.8x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 0.8x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 0.8x + x2 = 0 + 1.4 0.8x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 0.8x + x2 = 1.4 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 = 1.4 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 1.4 + 0.16 Combine like terms: 1.4 + 0.16 = 1.56 0.16 + 0.8x + x2 = 1.56 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (x + 0.4) equal to 1.2489996 and -1.2489996.Subproblem 1
x + 0.4 = 1.2489996 Simplifying x + 0.4 = 1.2489996 Reorder the terms: 0.4 + x = 1.2489996 Solving 0.4 + x = 1.2489996 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 = 1.2489996 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.2489996 + -0.4 x = 1.2489996 + -0.4 Combine like terms: 1.2489996 + -0.4 = 0.8489996 x = 0.8489996 Simplifying x = 0.8489996Subproblem 2
x + 0.4 = -1.2489996 Simplifying x + 0.4 = -1.2489996 Reorder the terms: 0.4 + x = -1.2489996 Solving 0.4 + x = -1.2489996 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 = -1.2489996 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.2489996 + -0.4 x = -1.2489996 + -0.4 Combine like terms: -1.2489996 + -0.4 = -1.6489996 x = -1.6489996 Simplifying x = -1.6489996Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8489996, -1.6489996}
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