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Simplifying 7 + -4x(2x + 5) = 4 Reorder the terms: 7 + -4x(5 + 2x) = 4 7 + (5 * -4x + 2x * -4x) = 4 7 + (-20x + -8x2) = 4 Solving 7 + -20x + -8x2 = 4 Solving for variable 'x'. Reorder the terms: 7 + -4 + -20x + -8x2 = 4 + -4 Combine like terms: 7 + -4 = 3 3 + -20x + -8x2 = 4 + -4 Combine like terms: 4 + -4 = 0 3 + -20x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + 2.5x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 2.5x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 2.5x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 2.5x + x2 = 0 + 0.375 2.5x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 2.5x + x2 = 0.375 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 0.375 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.375 + 1.5625 Combine like terms: 0.375 + 1.5625 = 1.9375 1.5625 + 2.5x + x2 = 1.9375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.9375 Calculate the square root of the right side: 1.391941091 Break this problem into two subproblems by setting (x + 1.25) equal to 1.391941091 and -1.391941091.Subproblem 1
x + 1.25 = 1.391941091 Simplifying x + 1.25 = 1.391941091 Reorder the terms: 1.25 + x = 1.391941091 Solving 1.25 + x = 1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.391941091 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.391941091 + -1.25 x = 1.391941091 + -1.25 Combine like terms: 1.391941091 + -1.25 = 0.141941091 x = 0.141941091 Simplifying x = 0.141941091Subproblem 2
x + 1.25 = -1.391941091 Simplifying x + 1.25 = -1.391941091 Reorder the terms: 1.25 + x = -1.391941091 Solving 1.25 + x = -1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.391941091 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.391941091 + -1.25 x = -1.391941091 + -1.25 Combine like terms: -1.391941091 + -1.25 = -2.641941091 x = -2.641941091 Simplifying x = -2.641941091Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.141941091, -2.641941091}
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