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Simplifying 4x(x + -2) = 7 Reorder the terms: 4x(-2 + x) = 7 (-2 * 4x + x * 4x) = 7 (-8x + 4x2) = 7 Solving -8x + 4x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -8x + 4x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -2x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -2x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -2x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -2x + x2 = 0 + 1.75 -2x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -2x + x2 = 1.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.75 + 1 Reorder the terms: 1 + -2x + x2 = 1.75 + 1 Combine like terms: 1.75 + 1 = 2.75 1 + -2x + x2 = 2.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -1) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -1 = 1.658312395 Simplifying x + -1 = 1.658312395 Reorder the terms: -1 + x = 1.658312395 Solving -1 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.658312395 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.658312395 + 1 x = 1.658312395 + 1 Combine like terms: 1.658312395 + 1 = 2.658312395 x = 2.658312395 Simplifying x = 2.658312395Subproblem 2
x + -1 = -1.658312395 Simplifying x + -1 = -1.658312395 Reorder the terms: -1 + x = -1.658312395 Solving -1 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.658312395 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.658312395 + 1 x = -1.658312395 + 1 Combine like terms: -1.658312395 + 1 = -0.658312395 x = -0.658312395 Simplifying x = -0.658312395Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.658312395, -0.658312395}
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