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Simplifying 6 + -3x(4x + -5) = 7 Reorder the terms: 6 + -3x(-5 + 4x) = 7 6 + (-5 * -3x + 4x * -3x) = 7 6 + (15x + -12x2) = 7 Solving 6 + 15x + -12x2 = 7 Solving for variable 'x'. Reorder the terms: 6 + -7 + 15x + -12x2 = 7 + -7 Combine like terms: 6 + -7 = -1 -1 + 15x + -12x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -1 + 15x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 0.08333333333 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + -1.25x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + -1.25x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + -1.25x + x2 = 0 + -0.08333333333 -1.25x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 -1.25x + x2 = -0.08333333333 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.08333333333 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.08333333333 + 0.390625 Combine like terms: -0.08333333333 + 0.390625 = 0.30729166667 0.390625 + -1.25x + x2 = 0.30729166667 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.30729166667 Calculate the square root of the right side: 0.554338946 Break this problem into two subproblems by setting (x + -0.625) equal to 0.554338946 and -0.554338946.Subproblem 1
x + -0.625 = 0.554338946 Simplifying x + -0.625 = 0.554338946 Reorder the terms: -0.625 + x = 0.554338946 Solving -0.625 + x = 0.554338946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.554338946 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.554338946 + 0.625 x = 0.554338946 + 0.625 Combine like terms: 0.554338946 + 0.625 = 1.179338946 x = 1.179338946 Simplifying x = 1.179338946Subproblem 2
x + -0.625 = -0.554338946 Simplifying x + -0.625 = -0.554338946 Reorder the terms: -0.625 + x = -0.554338946 Solving -0.625 + x = -0.554338946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.554338946 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.554338946 + 0.625 x = -0.554338946 + 0.625 Combine like terms: -0.554338946 + 0.625 = 0.070661054 x = 0.070661054 Simplifying x = 0.070661054Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.179338946, 0.070661054}
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